Question 9 :
Given the piece-wise function:
[tex]\begin{gathered} h(x)\text{ = }\frac{4}{3}x-2\text{ if x<0} \\ h(x)\text{ = -x + 1 if x }\ge\text{ 0} \end{gathered}[/tex]
First, we graph the function as shown below:
The domain is the set of allowed inputs or values in the x-axis:
Domain:
[tex](-\infty,\text{ }\infty)[/tex]
The range is the set of allowed outputs or values in the y-axis.
Range:
[tex](-\infty,\text{ 1\rbrack}[/tex]
Question 11:
Given the piece-wise function:
[tex]\begin{gathered} k(x)\text{ =x + 4 if x }<\text{ -1} \\ k(x)\text{ = }5\text{ if -1 }<\text{ x }<\text{ 2} \\ k(x)\text{ = }-\frac{1}{2}x\text{ + 1 if x}\ge\text{ 2} \end{gathered}[/tex]
The graph of the function is shown below:
The domain: when x= -1, the function is undefined
[tex](-\infty,\text{ -1) }\cup\text{ (-1 , }\infty)[/tex]
The range: At x=-1, the function is undefined.
[tex](-\infty\text{ , -1) }\cup\text{ 5}[/tex]
