Question

select the correct answer.
what is the range of this absolute value function?
graph of an absolute value function with vertex at (-6, 5), opening upwards
a. (-6 leq y < infty)
b. (-infty < y leq -6)
c. (5 leq y < infty)
d. (-infty < y < infty)

Explanation:

Step1: Recall range definition

Range is the set of all possible \( y \)-values of a function. For an absolute value function (a V - shaped graph), we look at the minimum \( y \)-value and how the graph extends.

Step2: Analyze the graph

The vertex (the lowest point) of the absolute - value graph has a \( y \)-coordinate of 5 (from the graph, we can see the minimum \( y \)-value is 5). Then, the graph opens upwards (since the two arms of the V - shape go up as we move away from the vertex), which means the \( y \)-values start at 5 and go to positive infinity. So the range is all real numbers \( y \) such that \( 5\leq y<\infty \).

Answer:

C. \( 5\leq y<\infty \)