Transformations of Graphs (Edexcel GCSE Maths: Higher)

The diagram shows part of the curve with equation .
The coordinates of the maximum point of the curve are (3, 5).

Write down the coordinates of the maximum point of the curve with equation

i)

[1]

ii)

[1]

iii)

[1]

The curve with equation  is transformed to give the curve with equation 

Describe the transformation.

The diagram shows a sketch of the graph of

Write down the coordinates of the point .

On the same diagram, draw a sketch of the graph of 

Here is the graph of  for  

On the grid, sketch the graph of  for 

Here is the graph of  for  

On the grid above, sketch the graph of for 

Here is the graph of  for  

On the grid above, sketch the graph of for 

The equation of a curve is 
is the point where the curve intersects the -axis.

State the coordinates of .

The equation of circle is 

The circle is translated by the vector  to give circle .

Draw a sketch of circle .

Label with coordinates
   the centre of circle
   and any points of intersection with the -axis.

The graph of  is shown on the grids.

On this grid, sketch the graph of 

On this grid, sketch the graph of 

The graph of  is shown on the grid.

On the grid above, sketch the graph of .

The graph of  is shown on the grid.

The graph G is a translation of the graph of 

Write down the equation of graph G.

Here is the graph of for

In parts (a) and (b) the graph of is shown as a dashed line.

On the grid below, draw the graph of  for 

On the grid below, draw the graph of 

Rita tries to draw the graph of for Here is her graph.

Give a reason why Rita’s graph is incorrect.

Here is a sketch of    

The curve passes through the points    (–2, –10)  (–1, –3)  (0, –2)  (1, –1)  (2, 6)

On the grid, sketch the curve 

The curve with equation    is reflected in the -axis.

Circle the equation of the reflected curve.

The graph of for  crosses the -axis in two places.

Write down the values of where this occurs.

...........................

Sketch the graph of  for .

The graph of  is shown on each of the grids.

On this grid, sketch the graph of

On this grid, sketch the graph of 

The graph of  is shown on both grids below

On the grid above, sketch the graph of

On this grid, sketch the graph of

This is a sketch of the curve with the equation 

The only minimum point of the curve is at .

Write down the coordinates of the minimum point of the curve with the equation

Write down the coordinates of the minimum point of the curve with the equation  

The graph of , where is a positive constant, is shown above.

Find the value of .

The graph of  for values of from  is shown above.

On the same axes, draw the graph of for values of from 

The graph of  is transformed to give the graph of 
The point on the graph of is mapped to the point on the graph of 

The coordinates of point are 
Find the coordinates of point .

The graph of the curve with equation  is transformed to give the graph of the curve with equation 

The point on with coordinates  is mapped to the point on .

Find the coordinates of .

The graph of intersects the -axis at two points.
The coordinates of the two points are (–1, 0) and (6, 0)

The graph of passes through the point with coordinates (2, 0), where is a constant.

Find the two possible values of .

The curve has equationwhere
The curve has equation where

By writing in the form , where and are constants, describe fully a series of transformations that map the curve onto the curve .

The curve has equation where

The point is the maximum point on .

Write down the coordinates of .

The curve is transformed to the curve by a translation of  Find an equation for the curve .

The curve is transformed to the curve .
The curve has equation

Describe fully the transformation that maps curve onto curve .

The graph of for is drawn on the grid below.

Find the value of , the value of and the value of .

a = .......................................................       
b = .......................................................         
c = .......................................................       

The equation of a curve is
The curve is transformed to curve under the translation

Find an equation of curve .

You do need to simplify the equation.

The graph of is translated 4 units to the right.

The translated graph has equation

Work out .

Give your answer in the form where and are integers.

Curve  has equation

Curve  is a reflection in the -axis of curve .

Work out the equation of curve .

Give your answer in the form         where  and  are integers.

For all values of

On the grid, draw the graph of the composite function    for