AnswersPrecalculusComparing a Function and Its Inverse — QuizQuestion 23
23
QuizMultiple Choice

Comparing a Function and Its Inverse — Quiz

Question 23 • Precalculus

Students are asked to graph the inverse, f inverse of x of an absolute value function, f of x after restricting its domain. The directions also ask that the graph include a dashed line that can be used to verify that the functions are inverses of each other. Which student’s work is correct?

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 straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma 1) and goes through (6 comma 7). The line (f inverse of x) originates from (0 comma negative 1) and goes through (7 comma 6). A dashed line with a positive slope passes through (0 comma 0) and (7 comma 7).
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 straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma negative 1) and goes through (6 comma 7). The line (f inverse of x) originates from (0 comma 1) and goes through (negative 6 comma negative 7). A dashed line with a negative slope passes through (0 comma 0) and (negative 7 comma 7).
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 straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma 1) and goes through (6 comma 7). The line (f inverse of x) originates from (0 comma 1) and goes through (negative 7 comma negative 6). A dashed line with a negative slope passes through (0 comma 0) and (negative 7 comma 7).
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 straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma 1) and goes through (6 comma 7). The line (f inverse of x) originates from (1 comma 0) and goes through (7 comma 6). A dashed line with a positive slope passes through (0 comma 0) and (7 comma 7).

Explanation

The shown branch of f goes from (0, 1) to (6, 7), so its rule is y = x + 1 for x ≥ 0. To find the inverse, swap x and y: x = y + 1, which gives y = x − 1, starting at (1, 0) and passing through (7, 6). The graphs of a function and its inverse reflect across the line y = x, so the dashed line should have positive slope through the origin. Choice C shows both the correct inverse and the dashed line y = x.

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