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GCSEMathsAQAExam Questions2. AlgebraGraphs of Functions

Graphs of Functions (AQA GCSE Maths)

Exam Questions

4 hours60 questions
Easy
Medium
Hard
1
Sme Calculator1 mark

Brogan needs to draw the graph of y space equals space x squared space plus space 1

Here is her graph.

q1-easy-2-17-graph-of-equation-edexcel-gcse-maths

Write down one thing that is wrong with Brogan's graph.

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2a
Sme Calculator2 marks

Complete the table of values for  y space equals space x cubed space long dash space 4 x

x negative 3 negative 2 negative 1 0 1 2 3
y     3 0     15

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2b
Sme Calculator2 marks

On the grid, draw the graph of space y space equals space x cubed space long dash space 4 x space from x space equals space minus 3 space to space x space equals 3

q2-easy-2-17-graph-of-equation-edexcel-gcse-maths

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3a
Sme Calculator2 marks

Complete the table of values for y space equals space x cubed space long dash space 3 x space plus space 1

x negative 2 negative 1 0 1 2
y   3     3

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3b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x cubed space long dash space 3 x space plus space 1 for values of x from long dash 2 space to space 2

q3-easy-2-17-graph-of-equation-edexcel-gcse-maths

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4a
Sme Calculator2 marks

Complete the table of values for y equals space 6 over x

x 0.5 1 2 3 4
 5
 6
y   6 3   1.5
   1

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4b
Sme Calculator2 marks

q4-easy-2-17-graph-of-equation-edexcel-gcse-maths

On the grid, draw the graph of y space equals space 6 over x space for space space 0.5 space less-than or slanted equal to space x space less-than or slanted equal to space 6

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5a
Sme Calculator2 marks

Complete the table of values for y space equals space 4 over x

x 0.5 1 2 4
 5
 8
y   4 2      

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5b
Sme Calculator2 marks

On the grid, draw the graph of space y space equals space 4 over x for 0.5 space less-than or slanted equal to space x space less-than or slanted equal to space 8

q5b-easy-2-17-graph-of-equation-edexcel-gcse-maths

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6a
Sme Calculator1 mark

The graph of y space equals space straight f left parenthesis x right parenthesis is drawn on the grid.

q6a-easy-2-17-graph-of-equation-edexcel-gcse-maths

Write down the coordinates of the turning point of the graph.

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6b
Sme Calculator1 mark

Write down the roots of straight f left parenthesis x right parenthesis space equals space 2

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6c
Sme Calculator1 mark

Write down the value of space straight f left parenthesis 0.5 right parenthesis

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7a
Sme Calculator1 mark

The graph of y space equals space straight f left parenthesis x right parenthesis is drawn on the grid.

q7a-easy-2-17-graph-of-equation-edexcel-gcse-maths

Write down the coordinates of the turning point of the graph.

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7b
Sme Calculator1 mark

Write down estimates for the roots of space straight f left parenthesis x right parenthesis equals 0

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7c
Sme Calculator1 mark

Use the graph to find an estimate for straight f left parenthesis 1.5 right parenthesis

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8
Sme Calculator1 mark

Here is a sketch of a graph.

q4-paper-1h-nov-2021-aqa-gcse-maths

Circle the equation of the graph.
k is a constant.

y equals k x y equals k plus x y equals k minus x y equals k over x

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9a
Sme Calculator1 mark

The equation of a curve is y space equals space 16 to the power of x

Circle the point that lies on the curve.

open parentheses 2 comma 32 close parentheses open parentheses 32 comma 2 close parentheses open parentheses 2 comma 256 close parentheses open parentheses 256 comma 2 close parentheses

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9b
Sme Calculator1 mark

A different point on the curve has y-coordinate 1 over 16

Work out the x-coordinate.

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10
Sme Calculator1 mark

Circle the point that is on the graph of y space equals space 1 over x

(–1, 1)  (0.3, 3) (0.8, 0.2) (2.5, 0.4)

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11
Sme Calculator1 mark

The equation of a curve is space y space equals space left parenthesis x space – space 1 right parenthesis squared space – space 6 space

Circle the coordinates of the turning point.

(–1, –6) (1, 6) (–1, 6) (1, –6)

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12
Sme Calculator1 mark

Here is the sketch of a graph.

q4-paper-2h-nov-2019-aqa-gcse-maths

Circle the equation of the graph.

y space equals space x y space equals space – x squared y space equals space – x cubed y space equals space 1 over x

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13
Sme Calculator1 mark

Here is a sketch of a quadratic curve.

The turning point is (3, –2)

q28-paper-3h-nov-2018-aqa-gcse-maths

Circle the correct statement about the gradient of the curve for x space less than space 3

gradient is positive gradient is negative
gradient is zero gradient could be any value

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14
Sme Calculator1 mark

Circle the word that describes the graph y space equals space sin space x

periodic exponential cubic quadratic

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15a
Sme Calculator2 marks

Complete the table of values for  y equals 1 over x open parentheses x squared plus 4 close parentheses

x 0.25 0.5 1 2 4 8
y 16.25         8.5

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15b
Sme Calculator2 marks

On the grid, draw the graph of  y equals 1 over x open parentheses x squared plus 4 close parentheses for 0.25 less-than or slanted equal to x less-than or slanted equal to 8

q15b-4ma1-2h-qp-june21-paper2-igcse-maths

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16
Sme Calculator3 marks

Here are six graphs.

q15-4ma1-2h-qp-jan20-paper2-igcse-maths

Complete the table below with the letter of the graph that could represent each given equation.

Write your answers on the dotted lines.

Equation Graph
y space equals space 2 over x squared ....................
y space equals space minus space 1 half x cubed ....................
y space equals space minus 5 over x ....................

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17a
Sme Calculator2 marks

The diagram shows part of a sketch of the curve space y space equals space sin space x degree

q16-paper2h-spec2016-edexcel-igcse-maths

Write down the coordinates of

i)
the point P

ii)
the point Q

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17b
Sme Calculator2 marks

Sketch the graph of y space equals space tan space x for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

Show the coordinates of any points of intersection with the coordinate axes.

q16b-paper2h-spec2016-edexcel-igcse-maths

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18a
Sme Calculator2 marks

Complete the table of values for y equals 6 over x

x 0.5 1 2 3 4 5 6
y   6   2     1

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18b
Sme Calculator2 marks

On the grid, draw the graph of  y equals 6 over x  for 0.5 less-than or slanted equal to x less-than or slanted equal to 6

q11b-4ma1-2hr-qp-jan22-paper2-igcse-maths

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19
Sme Calculator2 marks

Sketch the graph of y = 3x

Give the value of the y-intercept.

q17-paper4-nov2019-ocr-gcse-maths

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20
Sme Calculator2 marks

Shirley is asked to sketch a graph of  y = 5x for x > 0

She produces the following.

q13-paper5-june2019-ocr-gcse-maths

The graph has two errors.

How should they be corrected?

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21
Sme Calculator1 mark

The graph of y = x3 − x2 − 2 is drawn on the grid.

q19-paper5-june2019-ocr-gcse-maths

Use the graph to solve x3 − x2 − 2 = 0.
Give your answer correct to 1 decimal place.

x = ...................................................

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22
Sme Calculator2 marks

Here is the graph of   y = x2 + x − 6.

q10-paper4-nov2018-ocr-gcse-maths

Use the graph to solve the equation  x2 + x − 6  = 0.

x = ................. or x = ................

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23
Sme Calculator2 marks
i)
Sketch a graph on the axes that shows that y is directly proportional to x.

q4ai-paper4-spec2015-ocr-gcse-maths

[2]

ii)
Sketch a graph on the axes that shows y equals x cubed

q4aii-paper4-spec2015-ocr-gcse-maths
[2]

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1a
Sme Calculator2 marks

Complete the table of values for y space equals space 2 to the power of x

x negative 2 negative 1 0 1 2 3
y 0.25     2    

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1b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space 2 to the power of x for values of x from long dash 2 space to space 3

q1-medium-2-17-graph-of-equation-edexcel-gcse-maths

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2a
Sme Calculator2 marks

Complete the table of values for y space equals space x squared long dash x long dash space 6

x negative 3
 negative 2 negative 1 0 1 2 3
y 6     negative 6      

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2b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x squared space long dash x long dash space 6 for values of x from long dash 3 space to space 3

q2-medium-2-17-graph-of-equation-edexcel-gcse-maths

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2c
Sme Calculator2 marks

Use your graph to find estimates of the solutions to the equation space x squared space minus x minus 6 space space equals long dash 2

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3a
Sme Calculator1 mark

The diagram shows part of a sketch of the curve y space equals space sin space x to the power of ring operator.

q3-medium-2-17-graph-of-equation-edexcel-gcse-maths

Write down the coordinates of the point P.

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3b
Sme Calculator1 mark

Write down the coordinates of the point Q.

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4
Sme Calculator3 marks

Here are some graphs.

q4-medium-2-17-graph-of-equation-edexcel-gcse-maths

In the table below, match each equation with the letter of its graph.

Equation  Graph
y space equals space sin space x  
y space equals space x cubed space plus space 4 x  
y space equals space 2 to the power of x  
y space equals space 4 over x  

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5a
Sme Calculator2 marks

Complete the table of values for space y space equals space x squared minus 3 x space plus space 2

bold italic x negative 1 0 1 2 3 4 5
bold italic y 6       2   12

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5b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x squared space long dash space 3 x space plus space 2 for values of x from long dash 1 space to space 5

q5-medium-2-17-graph-of-equation-edexcel-gcse-maths

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5c
Sme Calculator2 marks

Find estimates for the solutions of the equation x squared space minus space 3 x space plus space 2 space equals space 4

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6a
Sme Calculator2 marks

Complete the table of values for y space equals space x squared space minus space 3 x space plus 1

x negative 2 negative 1 0 1 2 3 4
y 11   1 negative 1   1  

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6b
Sme Calculator2 marks

 On the grid, draw the graph of y space equals space x squared space long dash space 3 x space plus space 1 for values of x spacefrom long dash 2 space to space 4

q6-medium-2-17-graph-of-equation-edexcel-gcse-maths

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6c
Sme Calculator2 marks

By drawing a suitable straight line on the grid, find estimates for the solutions of

x squared space minus space 3 x space plus 1 space equals space 3

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7a
Sme Calculator2 marks

q7-medium-2-17-graph-of-equation-edexcel-gcse-maths

On the grid, draw the graph of space x squared space plus y squared space equals space 4

How did you do?

7b
Sme Calculator2 marks

Ox~7ekor_q7b-medium-2-17-graph-of-equation-edexcel-gcse-maths

On the grid, sketch the graph of y space equals space cos space x space for space 0 to the power of degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 to the power of degree

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8
Sme Calculator2 marks

Sketch the graph of y space equals space cos space x to the power of degree space end exponent space for space 0 space less-than or slanted equal to space x space less-than or slanted equal to space 360

q8-medium-2-17-graph-of-equation-edexcel-gcse-maths

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9a
Sme Calculator1 mark

Here is a sketch of space y space equals space cos space x spacefor values of x from 0° to 360°

q27-paper-1h-nov-2018-aqa-gcse-maths

alpha degree is an acute angle.
cos space alpha degree space equals space k

Circle the value of cos space left parenthesis 180 degree space – space alpha degree right parenthesis

1 space – space k k – k – 1 space – space k

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9b
Sme Calculator1 mark

Circle the value of cos spaceleft parenthesis 360 degree space plus space alpha degree right parenthesis

k space – space 1 k space plus space 1 – k k

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10
Sme Calculator1 mark

Circle the point that lies on the curve  y space equals space x squared space – space 4 x space plus space 1

(–1, 4) (–1, –4) (–1, –2) (–1, 6)

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11a
Sme Calculator2 marks

Part of the graph ofspace y space equals space 2 x squared minus space 4 x space minus space 1 space is shown on the grid.

q21-4ma1-2h-qp-jan22-paper2-igcse-maths

Use the graph to find estimates for the solutions of the equation 2 x to the power of 2 space end exponent minus space 4 x space minus space 1 space equals space 0

Give your solutions correct to one decimal place.

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11b
Sme Calculator3 marks

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation x to the power of 2 space end exponent minus space x space minus space 1 space equals space 0

Show your working clearly.

Give your solutions correct to one decimal place.

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12a
Sme Calculator1 mark

Complete the table of values for y space equals space x squared space – space 5 x space plus space 6

x 0 1 2 3 4 5
y 6   0 0 2  

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12b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x squared space – space 5 x space plus space 6 space for space 0 space less-than or slanted equal to space x space less-than or slanted equal to space 5

q6b-paper1h-jan2019-edexcel-igcse-maths

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12c
Sme Calculator3 marks

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation

x squared space – space 5 x space equals space x space – space 7

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13
Sme Calculator2 marks

The diagram shows the graph of y space equals space straight f space left parenthesis x right parenthesis for negative 4 space less-than or slanted equal to space x space less-than or slanted equal to space 12

jc9uPwkM_q18-4ma1-1hr-qp-jan20-paper1-igcse-maths

Note: Point P in the graph is from the previous question. It is not required for this question.

The equation straight f space left parenthesis x right parenthesis space equals space k has exactly two different solutions for negative 4 space less-than or slanted equal to space x space less-than or slanted equal to space 12

Use the graph to find the two possible values of k.

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14a
Sme Calculator3 marks

Write 3 x squared space minus space 12 x space plus space 7 in the form a left parenthesis x space plus space b right parenthesis squared space plus space c

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14b
Sme Calculator1 mark

The line bold L is the line of symmetry of the curve with equation y space equals space 3 x squared space minus space 12 x space plus space 7

Using your answer to part (a) or otherwise, write down an equation of bold L.

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15
Sme Calculator2 marks

Sketch the graph of y space equals sin space x for 0 degree less than x less than 360 degree

q13a-paper5-nov2020-ocr-gcse-maths

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16a
Sme Calculator2 marks

The number of gannets on an island is assumed to follow this exponential growth model.

N = 0.45 × 1.07x

N is the number of gannets, in thousands.
x is the number of years after 1st January 2010.

Complete the table for N = 0.45 × 1.07x.

x 0 5 10 15 20
N 0.45 0.63   1.24  

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16b
Sme Calculator2 marks

Draw the graph of straight N space equals space 0.45 space cross times 1.07 to the power of straight x

q21b-paper4-nov2018-ocr-gcse-maths

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16c
Sme Calculator2 marks

Use the graph to find the year when the gannet population is predicted to reach 1000.

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1a
Sme Calculator2 marks

On the grid, construct the graph of x squared space plus space y squared space equals space 16

q1-hard-2-17-graph-of-equation-edexcel-gcse-maths

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1b
Sme Calculator3 marks

Find estimates for the solutions of the simultaneous equations

table row cell x squared space plus space y squared space end cell equals cell space 16 end cell row cell y space end cell equals cell space 2 x plus 1 end cell end table

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2a
Sme Calculator2 marks

On the grid, draw the graph of x squared space plus space y squared space equals space 12.25

q2-hard-2-17-graph-of-equation-edexcel-gcse-maths

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2b
Sme Calculator3 marks

Hence find estimates for the solutions of the simultaneous equations

table row cell x squared space plus space y squared space end cell equals cell space 12.25 end cell row cell 2 x plus y end cell equals 1 end table

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3a
Sme Calculator2 marks

Complete the table of values for y space equals space x squared long dash space 2 x

x negative 2 negative 1 0 1 2 3 4
y   3 0     3  

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3b
Sme Calculator2 marks

On the grid, draw the graph of space y equals space x squared long dash space 2 x spacefor values of x from long dash 2 space to space 4

q3-hard-2-17-graph-of-equation-edexcel-gcse-maths

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3c
Sme Calculator2 marks

Solve  x squared minus 2 x minus 2 equals 1

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4a
Sme Calculator2 marks

Complete the table of values for y space equals space x squared long dash space 2 x long dash space 1

x negative 2 negative 1 0 1 2 3 4
y 7     negative 2 negative 1    

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4b
Sme Calculator2 marks

On the grid, draw the graph of  y space equals space x squared long dash space 2 x long dash space 1 for values of x from long dash 2 space to space 4

q4-hard-2-17-graph-of-equation-edexcel-gcse-maths

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4c
Sme Calculator2 marks

Solve   x squared space minus space 2 x space minus 1 space equals x plus 3

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5a
Sme Calculator3 marks

The diagram shows the graph of y space equals space x squared space long dash space 4 x space long dash space 2

q5-hard-2-17-graph-of-equation-edexcel-gcse-maths

Use the graph to find estimates for the solutions of

i)
x squared space minus 4 x space minus 2 space equals space 0
[1]
ii)
x squared space minus 4 x space minus 6 space equals 0
[2]

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5b
Sme Calculator3 marks

Use the graph to find estimates for the values of x that satisfy the simultaneous equations

table row cell y space end cell equals cell space x squared space long dash space 4 x space long dash space 2 end cell row blank blank blank row cell x space plus space y space end cell equals 6 end table

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6a
Sme Calculator2 marks

Construct the graph of space x squared space plus space y squared space equals space 9

q6-hard-2-17-graph-of-equation-edexcel-gcse-maths

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6b
Sme Calculator3 marks

By drawing the line x space plus space y space equals space 1 on the grid, solve the equations x squared space plus space y squared space equals space 9 x space plus space y space equals 1

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7
Sme Calculator2 marks

Here are four graphs.

q7-hard-2-17-graph-of-equation-edexcel-gcse-maths

The graphs represent four different types of function straight f.

Match each description of the function in the table to the letter of its graph.

Description of function Graph
straight f open parentheses x close parentheses is inversely proportional to x  
straight f open parentheses x close parentheses is a trigonometrical function  
straight f open parentheses x close parentheses is an exponential function  
straight f open parentheses x close parentheses is directly proportional to square root of x  

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8a
Sme Calculator2 marks

q8-hard-2-17-graph-of-equation-edexcel-gcse-maths

The graph of y space equals space k to the power of x, where k is a positive constant, is shown above.

Find the value of k.

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8b
Sme Calculator2 marks

q8b-hard-2-17-graph-of-equation-edexcel-gcse-maths

The graph of space y equals space sin space x degree space for values of x from space long dash 270 space to space plus 270 space is shown above.

On the same axes, draw the graph of y space equals space 1 space long dash space sin space x degree for values of x from long dash 270 space to space plus 270

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9
Sme Calculator1 mark

y is an obtuse angle.

Which statement is true?
Tick one box.

begin mathsize 26px style square end style sin space y space greater than space 0 and cos space y space greater than space 0
square sin space y space greater than space 0 spaceand cos space y space less than space 0
square sin space y space less than space 0 space andspace cos space y space greater than space 0
square sin space y space less than space 0 and cos space y space less than space 0

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10
Sme Calculator1 mark

straight f left parenthesis x right parenthesis space equals space sin left parenthesis x space – space 90 degree right parenthesis

Circle the value of f(0°)

1 0 negative 1 half -1

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11a
Sme Calculator1 mark

The curve C has equation y space equals space straight f left parenthesis x right parenthesis where straight f left parenthesis x right parenthesis space equals space 9 space – space 3 left parenthesis x space plus space 2 right parenthesis squared

The point A is the maximum point on bold C.

Write down the coordinates of A.

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11b
Sme Calculator1 mark

The curve bold C is transformed to the curve bold S by a translation of open parentheses table row 4 row 0 end table close parentheses
Find an equation for the curve bold S.

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11c
Sme Calculator1 mark

The curve bold C is transformed to the curve bold T.
The curve bold T has equation y space equals space 3 left parenthesis x space plus space 2 right parenthesis squared – space 9

Describe fully the transformation that maps curve bold C onto curve bold T.

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12
Sme Calculator4 marks

The curve bold space bold italic C bold spacehas equation y space equals space 4 left parenthesis x space minus space 1 right parenthesis squared space minus space a space   where a space greater than space 4

Using the axes below, sketch the curve bold italic C.
On your sketch show clearly, in terms of a,

i)
the coordinates of any points of intersection of bold italic C with the coordinate axes,

ii)
the coordinates of the turning point.
q20ii-4ma1-1h-qp-jan20-paper1-igcse-maths

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13a
Sme Calculator3 marks

Express 7 space plus space 12 x space – space 3 x squared in the form a space plus space b left parenthesis x space plus space c right parenthesis squared where a comma space b andspace c spaceare integers.

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13b
Sme Calculator1 mark

bold C is the curve with equationspace y space equals space 7 space plus space 12 x space – space 3 x squared space
The point A is the maximum point on bold C

Use your answer to part (a) to write down the coordinates of A

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14a
Sme Calculator2 marks

Complete the table of values for y space equals space x cubed – space 2 x squared – space 3 x space plus space 4

x -2 -1 -0.5 0 1 1.5 2 3
y     4.875 4   -1.625    

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14b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x cubed – space 2 x squared – space 3 x space plus space 4  for values of x from –2 to 3

q14b-paper2h-june2018-edexcel-igcse-maths

How did you do?

14c
Sme Calculator4 marks

By drawing a suitable straight line on the grid,
find estimates for the solutions of the equation x to the power of 3 space end exponent – space 2 x squared space – space x space plus space 1 space equals space 0

Give your solutions correct to 1 decimal place.

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15a
Sme Calculator2 marks

Complete the table of values for y space equals space 1 half space x cubed space – space 2 x space plus space 3

x – 3 –2 – 1 0 1 2 3
y – 4.5     3   3  

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15b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space 1 half space x cubed space – space 2 x space plus space 3 space for space – 3 space less-than or slanted equal to space x space less-than or slanted equal to space 3

q18b-paper2hr-nov2020-edexcel-igcse-maths

How did you do?

15c
Sme Calculator2 marks

By drawing a suitable straight line on the grid, find an estimate for the solution of the equation 1 half space x cubed space – space x space plus space 4 space equals space 0

x space equals............................................ 

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16
Sme Calculator1 mark

The curve bold C has equation y space equals space 3 space – space 5 left parenthesis x space plus space 1 right parenthesis squared
The point A is the maximum point on bold C.

Write down the coordinates of A.

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17
Sme Calculator6 marks

The curve C has equation y space equals space x squared space – space 6 x space plus space 4

Using the axes below, sketch the curve C.
On your sketch show clearly

i)
the exact coordinates of any points of intersection of C with the coordinate axes,

ii)
the coordinates of the turning point.

q21-paper1h-spec2016-edexcel-igcse-maths

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18a
Sme Calculator3 marks

Write begin mathsize 16px style x squared space plus space 4 x space minus space 16 end style in the form open parentheses x space plus space a close parentheses squared space minus space b.

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18b
Sme Calculator3 marks

Sketch the graph of y space equals space x squared space plus space 4 x space minus space 16 , showing clearly the coordinates of any turning points.

q18b-paper5-nov2018-ocr-gcse-maths

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19a
Sme Calculator3 marks

Write  x squared minus 10 x plus 22  in the form  open parentheses x minus a close parentheses squared minus b.

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19b
Sme Calculator4 marks

Sketch the graph of begin mathsize 16px style y equals x squared minus 10 x plus 22 end style .

Show clearly the coordinates of any turning points and the value of the begin mathsize 16px style y end style-intercept.

q19b-paper5-nov2020-ocr-gcse-maths

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20a
Sme Calculator2 marks

The graph of begin mathsize 16px style y space equals space 2 x squared space plus space 3 x space minus space 9 end style is drawn below.

q19-paper6-nov2020-ocr-gcse-maths

Use the graph to solve 2 x squared space plus space 3 x space minus space 9 space equals space 0.

x space equals space............................ space or x space equals space............................ space

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20b
Sme Calculator2 marks

The equation 2x2 + x − 4 = 0 can be solved by finding the intersection of the graph of y = 2x2 + 3x − 9  and the line y = ax + b.

i)
Find the value of a and the value of b.

table row a equals cell space............................. space space end cell row b equals cell.............................. space left square bracket 2 right square bracket end cell end table

ii)table row blank row blank end table

Hence use the graph to solve the equation 2x2 + x − 4 = 0.

x = ............................ or x = ............................[3]

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21a
Sme Calculator3 marks

Sketch the graph of y equals open parentheses x minus 2 close parentheses squared minus 3.
Show the coordinates of any turning points.

q19a-paper5-june2017-ocr-gcse-maths

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21b
Sme Calculator5 marks

The sketch shows part of a graph which has equation y equals a x squared plus b x plus c.

q19b-paper5-june2017-ocr-gcse-maths

Find the values of space a comma space b spaceand begin mathsize 16px style c end style.

a space equals space....................................... space b space equals space....................................... c space equals space.......................................

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