Question

what is the range for the following graph?
$(-infty, 0$
$(-infty, infty)$
$-4, 0$
$-12, 12$

Explanation:

Step1: Recall the definition of range

The range of a function is the set of all possible output values (y - values) the function can take.

Step2: Analyze the graph

From the graph (a wave - like graph touching the x - axis at the top and having a minimum point), we observe that the maximum y - value is 0 (since it touches the x - axis, \(y = 0\)) and the minimum y - value is - 4 (the lowest point of the wave has \(y=-4\)). Also, the graph is continuous between these values, so the range includes all values from - 4 to 0, including both endpoints.

Answer:

\([-4,0]\) (corresponding to the red option: \([-4, 0]\))