Question

Which graph is the graph of this function?

Answer 1

It's graph C. The < or > with no equality sign under them mean open circles on your graph. You have to look at it like this: for the first part of the piecewise, y = 5 (horizontal line at y = 5) between x values of -3 to -2, open circles on both. For the second part, y = -1.5 (horizontal line at y = -1.5) between x values of closed circle at -2 and open circle at 3. For the last part, y = 1/2 (horizontal line at y = 1/2) between x values of closed circle at 3 and closed circle at 4.

Answer 2

The graph that best represents the given function f(x) is:

Graph C.

Explanation:

We are given function f(x) as:

f(x)= 5 ; -3 < x < -2

-3/2 ; -2 ≤ x <3

1/2 ; 3 ≤ x ≤ 4

This means that a graph:

Is a straight horizontal line y=5 between -3 and -2 with open circles at -3 and -2 since the inequality is a strict inequality.

A straight horizontal line y= -3/2 between -2 and 3 with open circle at 3 and closed circle at 0.

A straight horizontal line y=1/2 between 3 and 4 with closed circles both at 3 and 4.( since the inequality is a inequality with a equality sign)

Hence, the graph is: Graph C.