Square Root and Cube Root Functions — Test

Question 15 • Algebra 2 with Probability

Which is the graph of g of x is equal to square root of x minus 16 end root ?

Answer

Image with description A coordinate plane with x-axis labeled from 4 to 44 in increments of 4 and y-axis labeled from 1 to 10 in increments of 1. A smooth curve originates from 16 comma 0, moves right and passes through the points 20 comma 2 and terminates at the point 40 comma 5.

Image with description A coordinate plane displays the x-axis labeled from 4 to 44 in increments of 4 and the y-axis labeled from 1 to 10 in increments of 1. An increasing curve begins at approximately 0 comma 4, rises steeply at first, then gradually levels off, passing near 4 comma 6, 12 comma 7.5, 24 comma 9, and ending at approximately 36 comma 10.

Image with description A coordinate plane with x-axis labeled from 4 to 44 in increments of 4 and y-axis labeled from 1 to 10 in increments of 1. A smooth curve originates from 4 comma 0, moves right and passes through the point 20 comma 4 and terminates at the point 40 comma 6.

Image with description A coordinate plane displays the x-axis labeled from 4 to 44 in increments of 4 and the y-axis labeled from 1 to 10 in increments of 1. An increasing curve begins at approximately 4 comma 4, rises steeply at first, then gradually levels off, passing near 8 comma 6, 16 comma 7.5, 28 comma 9, and ending at approximately 40 comma 10.

Explanation

For g(x) = √(x − 16), the expression under the square root must be nonnegative, so the graph begins at x = 16, where g(16) = 0. It also passes through (20, 2), since √(20 − 16) = 2, matching choice D.

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