Square Root and Absolute Value Functions — Test

Question 16 • Algebraic Reasoning

Which could be the graph of f of x is equal to start absolute value x minus h end absolute value plus k if h and k are both positive?

Answer

Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at 1 comma negative 4 and y-intercept at 0 comma negative 3.

Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at negative 4 comma negative 5 and y-intercept at 0 comma negative 1.

Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at 2 comma 1.

Image with description A coordinate plane with unlabeled axis. An absolute value graph with vertex at negative 3 comma 2 and y-intercept at 0 comma 5.

Explanation

The graph of f(x) = |x − h| + k has its vertex at (h, k). Since both h and k are positive, the vertex must have a positive x-coordinate and a positive y-coordinate. Choice C has vertex (2, 1), so it could be the graph.

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