Question

Which graph is the graph of this function?

Answer 1

Answer:

Graph C

Step-by-step explanation:

This piecewise function is composed of three straight lines of slope m = 0.

$5$        if        $-3 <x <-2$

$-\frac{3}{2}$     if        $-2 \leq x <3$

$\frac{1}{2}$        if        $3 \leq x \leq4$

Note that the line $y = -\frac{3}{2}$ is a horizontal line that intersects the y-axis in $-\frac{3}{2}$. that is to say -1.5

Therefore you can discard graph B and graph D because they do not show any line that cuts the y axis at -1.5.

We have the graph A and the graph C.

Note that for the line $y = -\frac{3}{2}$ the interval is $-2 \leq x <3$ or $[-2, 3)$.

That is, this interval does not include the number 3 but does include the number -2.

Note that graph A includes 3 but does not include -2. Therefore we can discard the graph A.

Then the correct option is graph C