Square Root and Cube Root Functions — Test

Question 22 • Algebra 2 with Probability

Which of the following is the graph of y is equal to square root of negative x minus 3 end root ?

Answer

Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve opens down and to the left in quadrant 2. The origin of the curve is (negative 3 comma 0) and passes through (negative 7 comma 2).

Image with description On a coordinate plane, the x and y axes range from negative 9 to 9 with increments of 1. The curve opens up and to the right in quadrants III and IV. The origin of the curve is negative 3 comma 0. The curve passes through the point 0 comma 1 point 6 and 6 comma negative 3, and end at 9 comma negative 3 point 5. The arrow is present on both end of the curve.

Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (3 comma 0) and passes through points (negative 1 comma 2) and (negative 6 comma 3) in the 2nd quadrant.

Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (3 comma 0) and decreases into the fourth quadrant. It passes through points (4 comma negative 1) and (7 comma negative 2).

Explanation

For y = √(-x - 3), the expression inside the square root must be nonnegative: -x - 3 ≥ 0, so x ≤ -3. The graph begins where the radicand is 0, at (-3, 0), and extends left and upward. For example, at x = -7, y = √(7 - 3) = 2, matching choice B.

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