Question

Consider the graph of the absolute value function g(x) below.

Answer 1

PART A.

According to the problem h(x) is a translation of g(x) 6 units down and 3 units left.

So, h(x) would be defined as

`h(x)=g(x+3)-6`

This equation shows both translations, x+3 represents 3 units to the left, and -6 outside the parenthesis represents 6 units down.

PART B.

Since h(x) would be an absolute value function, its domain would be all real numbers. However, its range would be all real numbers less than -2 because, with the 6 units downside movement, the range restriction changed from 4 to -2.

PART C.

Since h(x) is an absolute value function, we can deduct that it's not invertible because absolute value function inverse is not a function by definition.