Question

What is the range of the function graphed below?

Answer 1

second one

Explanation:

Answer 2

[-4,0) ∪ [2, ∞)

Explanation:

For piecewise function domain and range, we need to understand the difference between "(" and "[" or ")" and "]"

• The parenthesis ( "(" and ")" ) are used for "open circles" in the graph.
• The brackets ( "[" and "]" ) are use for "closed circles" in the graph.

Range is the set of y-values for which the function is defined.

Now,

The upper part of the function shows the graph going from y = 2 towards infinity (arrow). At y = 2 , there is closed circle, so this part range would be

[2, ∞) (infinity is always with parenthesis)

Now, looking at bottom part, the function is defined from 0 (open circle) to -4 (closed). so we can write:

[-4,0)

This is the range, 2nd answer choice is correct.

[-4,0) ∪ [2, ∞)