Question

select the correct answer.
what is the range of the function represented by this graph?
graph of a parabola opening downward with vertex, x-intercepts, and y-intercept
a. ( y leq 1 )
b. all real numbers
c. ( -4 leq y leq -2 )
d. ( y geq 1 )

Explanation:

Step1: Understand Range Definition

Range of a function is the set of all possible \( y \)-values (outputs) the function can take. For a graph, we look at the vertical extent (from lowest to highest \( y \)-value).

Step2: Analyze the Graph's Vertical Extent

The graph is a parabola opening downward (since it has a maximum point). The highest point (vertex) has a \( y \)-value of \( 1 \) (visually, the peak is at \( y = 1 \)). The graph extends downward infinitely (since it's a parabola opening down, the \( y \)-values go to \( -\infty \), but the maximum \( y \)-value is \( 1 \)). So the range includes all \( y \)-values less than or equal to \( 1 \).

Answer:

A. \( y \leq 1 \)