Question

Let f(x) = |x|, where x can be any real number. Write a formula for the function whose graph is the

transformation of the graph of f given by the instructions below.
b. A translation down 3 units

Answer 1

`g(x)=\mid x\mid -3`

Explanation:

We are given that a function

`f(x)=\mid x\mid` where x can be any real number.

We have to write the formula for the function whose graph is the transformation of the graph of f is given by a translation down 3 units.

When a translation down 3 unit then the transformation rule is given by

`(x,y)\rightarrow (x,y-3)`

Suppose
`y=f(x)`

After translation 3 units down then the value of y

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

Let
`g(x)=y-3=\mid x\mid -3`

Therefore, the formula for the function whose graph is the transformation of the graph of f is given by

`g(x)=\mid x\mid -3`