We are given the set {-2,-1,0,1,2} and the definition of piecewise function as follows
[tex]f(x)=\begin{cases}{-3\text{ if x<0}} \\ {-1\text{ if x=0}} \\ {x\text{ if x>0}}\end{cases}[/tex]
We only need to calculate the values of the function over the given set and then plot them. Note that as -2 and -1 are less than 0, if we want to calculate the value of f for these values, we should apply the first row of the definition of f. So we have that
[tex]\begin{gathered} f(\text{ -2\rparen= -3} \\ f(\text{ -1\rparen= -3} \end{gathered}[/tex]
when x=0 we are given the explicit value of the function. That is
[tex]f(0)=\text{ -1}[/tex]
Note that as 1 and 2 are greater than 0, we use the last row of the definition of f. That is, we output the same value as input. So we have
[tex]\begin{gathered} f(1)=1 \\ f(2)=2 \end{gathered}[/tex]
we collect this information on a table. So we get
x f(x)
-2 -3
-1 -3
0 -1
1 1
2 2
This can be summarized on the pair points (-2,-3), (-1,-3), (0,-1), (1,1) , (1,2).
If we plot this on a graph, we get
which corresponds to option C
