Question

Which graph is the graph of this function?

Answer 1

Graph C

Explanation:

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

`5` if
`-3 <x <-2`

`-(3)/(2)` if
`-2 \leq x <3`

`(1)/(2)` if
`3 \leq x \leq4`

Note that the line
`y = -(3)/(2)` is a horizontal line that intersects the y-axis in
`-(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 = -(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