Graph transformations

The lowest point of a curve is called a minimum point.

The diagram shows a sketch of the curve with equation y = f ()x. The minimum point of the curve has coordinates (6, –3).

For each of the following equations, write down the coordinates of the minimum point of the curve.

y = 4 f ()x

The coordinates of the minimum point are (_{……........ …..},_{……........ ….}).

y = f (x + 2)

The coordinates of the minimum point are (_{……........ ….},_{……........ ….}).

The curve with equation y = f ()x is reflected in the x-axis. Write down the equation of the transformed curve.

You should use function notation.

The following diagram shows a sketch of y = cos x for values of x from 0° to 360°.

The highest point of a curve is called a maximum point. The diagram below shows a sketch of the curve with equation y = f(x). The maximum point of this curve has coordinates (−2, 5).

On the same diagram, sketch the curve y = f(x − 6). Mark clearly the coordinates of any point where the new curve crosses an axis.

Complete the following sentence.

The maximum point of the curve y = f(x − 6) has coordinates_........

The diagram shows a sketch of y = f (x).

The point where the curve has a gradient of 0 is labelled A and has coordinates (8, –1).

On the axes below, sketch the curve y = f (x + 3). You must: • indicate the coordinates of any point where the new curve crosses an axis

• complete the coordinates of the point on the curve where the gradient is 0.

The coordinates of the point on the curve where the gradient is 0 are (_{……........ …..……},_{………........ …..……}).

The following diagram shows a sketch of y sin x for values of x from 0° to 360°.

Given that sin62° = 0·8829, correct to 4 decimal places, write down all the solutions of the equation

for values of x from 0° to 360°.

Use the following axes to sketch the graph of y –sin x for values of x from 0° to

360°. You must indicate any important values on the y-axis.

Use the following axes to sketch the graph of y sin x + 1 for values of x from 0°

to 360°. You must indicate any important values on the y-axis.

The highest point of a curve is called a maximum point.

The diagram below shows a sketch of the curve with equation y f x. The maximum point of this curve has coordinates (–5, 4).

For each of the following, write down the coordinates of the maximum point of the curve with the given equation.

y 2 f x

The coordinates of the maximum point are (_........ ,_........ ).

y f x 7

The coordinates of the maximum point are (_........ ,_........ ).

The curve with equation y f x is reflected in the y-axis. Write down the equation of the transformed curve.

You should use function notation.

The equation of the transformed curve is

The following diagram shows a sketch of the curvey f x.

The curve is transformed, as shown below.

Using function notation, complete the equation of the transformed curve.

The following diagram shows a sketch of the curve y f x.

The curve is transformed, as shown below.

Using function notation, complete the equation of the transformed curve.

The following diagram shows a sketch of the curve y = f (x).

In each of the following questions, the graph of y = f(x) has been transformed.

Circle the only possible equation of the transformed curve.

The following diagram shows a sketch of the curve y = f (x).

The curve is transformed, as shown below.

Using function notation, complete the equation of the transformed curve.

The following diagram again shows a sketch of the curve y = f(x).

The curve is transformed, as shown below.

Using function notation, complete the equation of the transformed curve.

The following graph represents the curve y = f (x).

There are 9 equations and 4 graphs of different transformations of y = f(x) shown below. Choose the equation which describes each transformation of y = f(x). Write it in the box provided.

One has been completed for you.

The following diagram shows a sketch of the curve y = f (x).

The curve is transformed, as shown below. y

Using function notation, complete the equation of the transformed curve.

The following diagram again shows a sketch of the curve y = f(x).

The curve is transformed, as shown below. y

Using function notation, complete the equation of the transformed curve.

The graph shows a sketch of the curve with equation y = x² + 2.

The lowest point of the curve has coordinates (0, 2).

On the same axes, sketch the graph of the curve with equation y = (x – 4)² + 2.

Indicate clearly the coordinates of the lowest point on the new curve.

Given that cos 21° = 0.9336, correct to 4 decimal places, write down all the solutions of the equation

for values of x from 0° to 360°.

A sketch of the graph y = f (x) is shown below.

Two specific points are shown on the graph. They are called a maximum point and a minimum point. The maximum point shown is (–2, 2) and the minimum point shown is (2, –2).

The graphs on the opposite page are transformations of y = f(x). Draw a line connecting each graph to the equation describing the transformation.

One has been done for you.