Notice that the expression for h(x) uses an absolute value. The absolute value is the basic function related to h(x).
Recall the following function transformations:
Horizontal shift by c units:
[tex]f(x)\rightarrow f(x-c)[/tex]
Vertical shift by c units:
[tex]f(x)\rightarrow f(x)+c[/tex]
Reflection across the X axis:
[tex]f(x)\rightarrow-f(x)[/tex]
Starting with the absolute value function, notice that the function h can be obtained by applying a reflection across the X-axis, a horizontal shift by 1 unit and a vertical shift by 4 units:
[tex]undefined[/tex]
