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GCSEMathsAQAHigherFlashcards2. AlgebraGraphs of Functions

Graphs of Functions (AQA GCSE Maths)

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  • FrontTypes of Graphs

    Why does the graph of y equals 1 over x not touch the y-axis?

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  • Why does the graph of y equals 1 over x not touch the y-axis?

    The graph of y equals 1 over x does not touch the y-axis because on the y-axis, x equals 0. You cannot divide by zero, therefore the graph does not have any values on the y-axis.

  • True or False?

    y equals a k to the power of x is an example of an exponential graph.

    True.

    y equals a k to the power of x is an example of an exponential graph; it has a variable power.
    E.g. y equals 2 cross times 3 to the power of x

  • What is an asymptote?

    An asymptote is a line on a graph that a curve gets closer and closer to but never touches.

    These may be horizontal or vertical.

    E.g. y equals 1 over x has asymptotes at y equals 0 and x equals 0.

  • Will the vertex of the graph y equals negative x squared plus x plus 5 be a maximum or a minimum point?

    The vertex of the graph y equals negative x squared plus x plus 5 will be a maximum point.

    The vertex of a quadratic graph will be a maximum point if the coefficient of x squared is negative. The graph is n-shaped.

  • Where does the graph of y equals 3 open parentheses x minus 1 close parentheses open parentheses x plus 2 close parentheses cross the x-axis?

    The graph of y equals 3 open parentheses x minus 1 close parentheses open parentheses x plus 2 close parentheses crosses the x-axis at open parentheses 1 comma space 0 close parentheses and open parentheses negative 2 comma space 0 close parentheses.

    To find these roots, make each factor equal to zero to find the x-coordinate:

    • x minus 1 equals 0 gives x equals 1

    • x plus 2 equals 0 gives x equals negative 2

  • How can you find the coordinates of the turning point of a quadratic graph?

    To find the coordinates of the turning point of a quadratic graph, you can complete the square (writing in the form a open parentheses x minus b close parentheses squared plus c)

    open parentheses b comma c close parentheses will be the turning point.

  • True or False?

    The turning point of y equals 4 minus open parentheses x minus 1 close parentheses squared is at the point open parentheses 4 comma space 1 close parentheses.

    False.

    The turning point of y equals 4 minus open parentheses x minus 1 close parentheses squared is not at the point open parentheses 4 comma space 1 close parentheses.

    The x-coordinate is the value that makes the squared bracket equal to zero.

    The coordinates should be open parentheses 1 comma space 4 close parentheses.

  • True or False?

    You should always use a ruler when plotting the graph of a function.

    False.

    You should only use a ruler if a graph is linear (and for drawing the axes if they are not given).

    For curves, draw a single smooth freehand curve.

  • How would you find the y-intercept of a graph using its equation?

    To find the y-intercept of a graph, you would substitute x equals 0 into the equation.

  • True or False?

    The solutions to x cubed minus 4 x equals 0 are the value(s) where the graph of y equals x cubed minus 4 x crosses the y-axis.

    False.

    The solutions to x cubed minus 4 x equals 0 are not the value(s) where the graph of y equals x cubed minus 4 x crosses the y-axis.

    x cubed minus 4 x equals 0 when y equals 0 which is the x-axis. Therefore the solutions are the values where the graph crosses the x-axis.

  • The solutions of x cubed plus x squared minus 3 equals x minus 2 are the x values of the intersections between y equals x cubed plus x squared minus 3 and which other graph?

    The solutions of x cubed plus x squared minus 3 equals x minus 2 are the x values of the intersections between y equals x cubed plus x squared minus 3 and bold italic y bold equals bold italic x bold minus bold 2.

  • True or False?

    The x values of the intersections of the two graphs y equals x plus 1 and y equals x squared plus 5 x plus 4 are the solutions of x squared plus 4 x plus 3 equals 0.

    True.

    The x values of the intersections of the two graphs y equals x plus 1 and y equals x squared plus 5 x plus 4 are the solutions of x squared plus 4 x plus 3 equals 0.

    Set the equations equal to each other and rearrange: x squared plus 5 x plus 4 equals x plus 1.

  • What is the graph of y equals sin x for negative 360 degree less or equal than x less or equal than 360 degree?

    The graph of y equals sin x for negative 360 degree less or equal than x less or equal than 360 degree is:

    Graph of y = sin x.

  • What is the graph of y equals cos x for negative 360 degree less or equal than x less or equal than 360 degree?

    The graph of y equals cos x for negative 360 degree less or equal than x less or equal than 360 degree is:

    Graph of y = cos x.

  • What is the graph of y equals tan x for negative 360 degree less or equal than x less or equal than 360 degree?

    The graph of y equals tan x for negative 360 degree less or equal than x less or equal than 360 degree is:

    Graph of y = tan x.

  • True or False?

    The point open parentheses 0 comma space 0 close parentheses lies on the graph y equals sin x.

    True.

    The point open parentheses 0 comma space 0 close parentheses lies on the graph y equals sin x.

  • What is the y-intercept of the graph y equals cos x?

    The y-intercept of the graph y equals cos x is open parentheses 0 comma space 1 close parentheses.

  • What is the minimum y value of the graph y equals sin x?

    The minimum y value of the graph y equals sin x is -1.

  • True or False?

    The graph y equals cos x repeats itself every 180°.

    False.

    The graph y equals cos x does not repeat itself every 180°.

    It repeats itself every 360°.

  • True or False?

    The graph y equals tan x repeats itself every 180°.

    True.

    The graph y equals tan x repeats itself every 180°.

  • The graph y equals sin x repeats itself every how many degrees?

    The graph y equals sin x repeats itself every 360°.

  • True or False?

    The maximum y value on the graph y equals tan x is 1.

    False.

    The maximum y value on the graph y equals tan x is not 1.

    The graph y equals tan x does not have a maximum value.

  • How would you use a graph of y equals sin x to find the solutions of sin x equals 0.5 for 0 degree less or equal than x less or equal than 360 degree?

    To find the solutions of sin x equals 0.5 for 0 degree less or equal than x less or equal than 360 degree using the graph y equals sin x:

    • calculate one solution using inverse trig x equals sin to the power of negative 1 end exponent open parentheses 0.5 close parentheses

    • draw the horizontal line y equals 0.5

    • use the symmetry of the graph to find the other solution

    Graph of y = sin x. A vertical line at 30º on the x-axis meets the curve at y = 0.5. A horizontal line is drawn across from this point until it touches the curve again and a vertical line is drawn down from here until it meets the x-axis at 150º.

  • True or False?

    After finding the first solution for an equation involving the cosine function, you can find another solution by subtracting the first solution from 180º.

    False.

    After finding the first solution for an equation involving the cosine function, you can find another solution by subtracting the first solution from 360º.

    The cosine graph showing that to find a second solution to an equation involving cos can be done by subtracting the first solution from 360º.

  • What angle should you add to or subtract from a first solution to find another solution for an equation involving the tangent function?

    If you know a first solution for an equation involving the tangent function, you can add to or subtract 180º from it to find another solution .

    The graph y = tan x showing that you can add 180º to find another solution from a first solution.
Previous:Linear GraphsNext:Equation of a Circle

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation