Explanation
A piecewise function is a function that is defined by different formulas or functions for each given interval.
So for the piecewise function given
[tex]f(x)=\begin{cases}{\frac{1}{2}x+4,\text{ x}\leq-2} \\ {} \\ {-x,\text{ x>-2}}\end{cases}[/tex]
To plot the graph of the functions on the same axis
for the first function
[tex]\begin{gathered} f(x)=\frac{1}{2}x+4 \\ we\text{ can find the value of f\lparen x\rparen, when x = -2,-3,-4} \\ when\text{ x=-2, f\lparen x\rparen=3} \\ when\text{ x=-3, f\lparen x\rparen=2.5} \\ when\text{ x=-4, f\lparen x\rparen=2} \end{gathered}[/tex]
For the second function
[tex]\begin{gathered} we\text{ can use when x = -1, y=-1} \\ when\text{ x=0, y=0} \\ \end{gathered}[/tex]
We can plot the x and f(x) coordiantes as:
in selecting the correct answer, we will have graph A as the correct graph
The answer is option A
