Comparing a Function and Its Inverse — Quiz

Question 17 • Precalculus

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

Answer

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 that passes through (0 comma 1) and (negative 6 comma 7) with a negative slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

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 that passes through the origin with a negative slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

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 that passes through (0 comma 1) and (6 comma 7) with a positive slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

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 that passes through the origin with a positive slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

Explanation

A function and its inverse have their coordinates swapped: for example, (0, 1) on the first curve corresponds to (1, 0) on the second, and (2, 3) corresponds to (3, 2). Inverse graphs are reflections across the line y = x, which passes through the origin with positive slope. Choice A shows that dashed line.

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