Absolute Value Functions and Translations Answers

Which phrases describe the graph of f(x) = |x| ? Check all that apply.

{y | y is all real numbers}{y | y is greater than zero}✔ {y | y is greater than or equal to zero}

constantdecreasing✔ increasing

constant✔ decreasingincreasing

Complete the statements for the graph of f(x) = |x|.

Complete the statements for the graph of f(x) = |x|.

The vertex of the graph of f(x) = |x – 3| + 6 is located at ([___] , [___] ).

(2, 1)✔ (–2, 1)(1, 2)(–1, –2)

The graph shows f(x) = |x – h| + k. What is the value of h?h = 2.5h = –1.5h = 1.5h = –2.5

Which function is represented by the graph?f(x) = |x – 1| + 3f(x) = |x + 1| – 3f(x) = |x – 1| – 3f(x) = |x + 1| + 3

On which interval is the function increasing?(–∞, –4)(–∞, 4)(–4, ∞)(4, ∞)

What are the domain and range of f(x) = |x – 3 | + 6? Domain: {x | x is all real numbers}Range: {y | y ≥ 6}Domain: {x | x ≥ 3}Range: {y | y ≥ 6}Domain: {x | x is all real numbers}Range: {y | y ≥ – 6}Domain: {x | x ≥ 3}Range: {y | y ≥ – 6}

The graph of f(x) = |x| has been translated left 2 units and up 1 unit. If no other transformations of the function have occurred, which point lies on the new graph?(–4, 2)(–3, 1)( –2, 5)( –1, 2)

The vertex of the graph of f(x) = |x – 3| + 6 is located at ([___] , [___] ).