Question

determine the range of the function graphed below.
options:
$(-5, 5)$
$-7, -2$
$-5, 5$
$(-7, -2)$

Explanation:

Step1: Recall Range Definition

Range is the set of all y - values the function takes. For a graph, we look at the vertical extent (minimum and maximum y - values).

Step2: Identify Minimum Y - Value

The lowest point on the graph (vertex) is at \(y=-7\) (since the point is \((0, - 7)\) or we can see from the grid that the bottom of the parabola - like graph is at \(y = - 7\)).

Step3: Identify Maximum Y - Value

The highest points on the graph are the endpoints, which have a y - value of \(-2\) (the blue dots are at \(y=-2\)).

Step4: Determine the Interval

Since the graph includes the endpoints (the dots are filled, so the function includes \(y=-7\) and \(y = - 2\)), the range is from \(-7\) to \(-2\) inclusive. So the range is \([-7,-2]\).

Answer:

\([-7, - 2]\) (corresponding to the option \([-7, - 2]\))