Problem

Derive the exact graph fingerprint for \(y=2|x-4|-1\). Identify the translations and vertical scale, locate the vertex, determine opening, domain, and range, and verify the fingerprint by evaluating symmetric inputs \(x=3\) and \(x=5\).

Answer choices

Choose your path.

Preview only

Absolute-value graph shifted right 4 and down 1 with no stretch; vertex (4,−1); opens up; domain all real; range [−1,∞); points (3,0), (5,0).

Absolute-value graph shifted left 4 and down 1 with vertical stretch 2; vertex (−4,−1); opens up; domain all real; range [−1,∞); points (−5,1), (−3,1).

Absolute-value graph shifted right 4 and up 1 with vertical stretch 2; vertex (4,1); opens up; domain all real; range [1,∞); points (3,3), (5,3).

Absolute-value graph shifted right 4 and down 1 with vertical stretch 2; vertex (4,−1); opens up; domain all real; range [−1,∞); points (3,1), (5,1).

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Derive the exact graph fingerprint for \(y=2|x-4|-1\). Identify the translations and vertical scale, locate the vertex, determine opening, domain, and range, and verify the fingerprint by evaluating symmetric inputs \(x=3\) and \(x=5\).

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.