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.

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

The function is

vertical stretched by a factor of 3reflected across y-axishorizontal stretched by a factor of 5horizontal translated to the left 1/5 units

Step-by-step 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-axisf(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)