9
QuizMultiple Choice

N/A — Exam

Question 9 • Algebraic Reasoning

Which graph includes a function, its inverse, and a dashed line that verifies the relationship?

Answer
A
Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A horizontal dashed line at y equals 1.
B
Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A dashed vertical line at x equals 1.
C
Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A dashed line with a negative slope passes through (5 comma negative 5), the origin, and (negative 5 comma 5).
D
Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A dashed line with a positive slope passes through (negative 5 comma negative 5), the origin, and (5 comma 5).

Explanation

A function and its inverse are reflections of each other across the line y = x, which has positive slope and passes through the origin. The listed points support this relationship: (0, 1) on one curve corresponds to (1, 0) on the other, and (-2, 0) corresponds to (0, -2). Choice D shows the dashed line through (-5, -5), the origin, and (5, 5), so it verifies the inverse relationship.

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