Graphing Transformation

Lesson 6: More Examples

Example 1

Given the graph of y = f (x),

Sketch the graphs of

(a)

(b)

Solution

(a)

We will apply the transformation in the order:

Note: If we switch the order of transformation, we will get

(b)

We will apply the transformation in the order:

Note: If we switch the order of transformation, we will get

Example 2

The transformations A, B and C are given as follows:

A:

Reflection about the y axis.

B:

C:

Translation of 4 units in the positive x direction.

Scaling parallel to the y axis by factor 2.

A curve undergoes in succession, the transformations A, B and C and the equation of the resulting curve is               . Determine the equation of the curve before the transformations were applied.

Solution

Let A', B' and C' be the reverse transformations of A, B and C respectively.

We will apply the transformations in the order

A':

Reflection about the y axis.

B':

C':

Translation of 4 units in the negative x direction.

Scaling parallel to the y axis by factor 0.5.

Replace y with 2y

Replace x with x + 4

Replace x with -x

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