8
QuizMultiple Choice

Absolute Value Functions and Translations — Quiz

Question 8 • Mathematics II

The graph of f of x is equal to absolute value of x is transformed to g of x is equal to start absolute value x plus 1 end absolute value minus 7 On which interval is the function decreasing?

Answer
A
open paren negative infinity comma 7 close paren
B
open paren negative infinity comma 1 close paren
C
open paren negative infinity comma negative 1 close paren
D
open paren negative infinity comma negative 7 close paren

Explanation

The graph of g(x) = |x + 1| - 7 is a V-shape opening upward, with its vertex at x = -1. As x increases toward -1 from the left, the function’s values decrease, so g is decreasing on (-∞, -1). The vertical shift by -7 changes the height of the graph but not where it is decreasing.

AI-written and checked against the verified answer.

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