Absolute Value Functions — Quiz

Question 6 • Algebraic Reasoning

What are the domain and range of f of x is equal to 2 start absolute value x minus 4 end absolute value ?

Answer

domain: open paren negative infinity comma infinity close paren ; range: f of x is greater than or equal to 0

domain: x is greater than or equal to 2 ; range: open paren negative infinity comma infinity close paren

domain: open paren negative infinity comma infinity close paren ; range: f of x is less than or equal to 0

domain: x is less than or equal to 2 ; range: open paren negative infinity comma infinity close paren

Explanation

The absolute value expression |x − 4| is defined for every real number x, so the domain is all real numbers, or (−∞, ∞). Since |x − 4| is always at least 0, multiplying it by 2 keeps the output nonnegative. The smallest value is 0, reached when x = 4, so the range is f(x) ≥ 0. This matches choice A.

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