Question

what is the range of the graph? #12
a $(-7, -1)$
b $(-6, 6)$
c $-7, -1$
d $-6, 6$
(graph of an ellipse on a coordinate grid; options a, b, c, d with circular selection buttons below)

Explanation:

Step1: Recall range definition

Range is the set of all y - values the graph covers. For a graph (here an ellipse), we look at the minimum and maximum y - coordinates, including the endpoints (since the ellipse is a closed curve, the endpoints are included, so we use square brackets).

Step2: Analyze the ellipse's y - values

Looking at the ellipse, the lowest y - value (minimum) and highest y - value (maximum) should be determined. From the options, option C is \([-7, - 1]\) which would represent the range (y - values) of the ellipse. Let's check the options:

• Option A: \((-7,-1)\) is an open interval, but the ellipse includes its endpoints, so A is wrong.
• Option B: \((-6,6)\) is an open interval and the y - values here don't match the ellipse's vertical extent.
• Option D: \([-6,6]\) is about x - values (domain) or incorrect y - values.
• Option C: \([-7,-1]\) is a closed interval, representing the set of all y - values from - 7 to - 1, including both, which matches the ellipse's vertical range.

Answer:

C. \([-7, - 1]\)