Question

Let f(x) = |x| for all real numbers x. Write the formula for the function represented by the described

transformation of the graph of y = f(x).
a. First, a vertical stretch with scale factor 1 / 3 is performed, then a translation right 3 units, and finally a translation
down 1 unit.

Answer 1

`y=((1)/(3)f(x-3))-1`

Explanation:

Please see the picture below.

1. Given the function f(x) = |x|, applying a vertical stretch with scale factor
`(1)/(3)`, we have the transformed function:

`y=(1)/(3)f(x)`

2. Applying a translation of 3 units to the right, we have:

`y=(1)/(3)f(x-3)`

3. Finally applying a translation down of 1 unit, we have:

`y=((1)/(3)f(x-3))-1`