AnswersAlgebraic ReasoningSquare Root and Absolute Value Functions — TestQuestion 19
19
QuizMultiple Choice

Square Root and Absolute Value Functions — Test

Question 19 • Algebraic Reasoning

On each coordinate plane, the parent function f of x is equal to absolute value of x is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g of x is equal to absolute value of x minus 4 as a solid line?

Answer
A
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 0 comma negative 4, and passes through the points negative 4 comma 0 and 4 comma 0.
B
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 4 comma 0, and passes through the points 2 comma 2 and 6 comma 2.
C
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at negative 4 comma 0, and passes through the points negative 6 comma 2 and negative 2 comma 2.
D
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 0 comma 4, and passes through the points negative 2 comma 6 and 2 comma 6.

Explanation

In g(x) = |x − 4|, subtracting 4 inside the absolute value shifts the parent graph y = |x| four units to the right. Its vertex moves from (0, 0) to (4, 0), and points two units from the vertex have y-coordinate 2, such as (2, 2) and (6, 2). This matches choice B.

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