Question

which graph has the following range? 0, 7
a
b
c
d
#30
a
b
c
d

Explanation:

Step1: Recall Range Definition

The range of a graph (in terms of \( y \)-values) is the set of all possible output values. The interval \([0, 7]\) means \( y \) starts at \( 0 \) (inclusive) and goes up to \( 7 \) (inclusive), so the graph should have a minimum \( y \)-value of \( 0 \) and a maximum \( y \)-value of \( 7 \), with no \( y \)-values below \( 0 \).

Step2: Analyze Each Graph

• Graph A: A circle centered such that \( y \)-values likely span below \( 0 \) (since it's symmetric vertically across a horizontal line, probably the \( x \)-axis or near it), so range includes negative \( y \)-values. Eliminate A.
• Graph B: An ellipse or curve symmetric vertically but likely has \( y \)-values below \( 0 \) (since it's centered around a vertical line, but the bottom part would be below \( y = 0 \)). Eliminate B.
• Graph C: An ellipse symmetric vertically, so \( y \)-values would be symmetric around a horizontal line, likely including negative \( y \)-values. Eliminate C.
• Graph D: The graph (a circle or curve) is positioned with the bottom at \( y = 0 \) and top at \( y = 7 \) (visually, it doesn't go below \( y = 0 \)). So its \( y \)-values are from \( 0 \) to \( 7 \), matching the range \([0, 7]\).

Answer:

D