Question

Y = f(x). Replace, in the following order: x with – 1/5x,

x, x with x – 1, and y with
1/3y. Describe the transformation in terms of the function and in terms of its effect on the graph.

Answer 1

y = 3f(-1/5x + 1/5)

The function is

• vertical stretched by a factor of 3
• reflected across y-axis

• horizontal stretched by a factor of 5

• horizontal translated to the left 1/5 units

Explanation:

Starting with: y = f(x)

Replacing x with -1/5x: y = f(-1/5x)

Replacing x with x - 1: y = f(-1/5(x - 1)) = f(-1/5x + 1/5)

Replacing y with 1/3y: 1/3y = f(-1/5x + 1/5) or y = 3f(-1/5x + 1/5)

The transformation:

• kf(x) vertically stretches the function by a factor of k (here k is 3)

• f(-x) reflects the function across y-axis

• f(bx) horizontally stretches the function by a factor of 1/b (here b is 1/5)

• f(x + c) horizontally translates the function left c units (here c is 1/5 units)