Transformations of Graphs

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  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 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 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 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 function f() is defined as ƒ () = 3 − 8 − 2

Find the coordinates of the turning point on the graph of  =

Using your result from part (a) write down the coordinates of the turning point on the following graphs:

 =  +2

[1]

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 

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 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.

The graph of    for  is drawn on the grid below.

Given that and that

find the value of a and the value of .

The graph of is shown on the grid below.

On the grid, sketch the graph of for

The graph of  is shown on the grid.

On the grid above, sketch the graph of 

The graph of  is shown on the grid below.

Write down the value of 

The diagram shows part of the curve with equation 

The coordinates of the minimum point on this curve are (3, –4)

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

(iii)

[1]

The curve with equation   is translated to give curve .

 has a minimum at the point with coordinates (3, 5)

The equation of  is 

Write down the value of .

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

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 .