Question

Write a formula for the function g(x) obtained when the graph of f(x)=|x| is shifted down 6 units and to the right 11 units.

Answer 1

Explanation:

When f(x) is shifted down 6 units, the transformation mapping is:

`f(x)\to f(x)-6`

Next, if the result is shifted to the right 11 units, we have:

`f(x)-6\to f(x-11)-6`

Given that f(x)=|x|, the formula for g(x) is given below:

`\begin{gathered} f(x)=|x| \\ \implies g(x)=f(x-11_{})-6 \\ \implies g(x)=|x-11|-6 \end{gathered}`

The formula for g(x) is