Radical Functions and Introduction to Proof — Test

Question 12 • CMS 2026-2027 NC Math 2 CREDIT RECOVERY

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 8 to 8 in increments of 1. The curve opens up and to the right in quadrants 3 and 4. The origin of the curve is (negative 3 comma 0) and the curve passes through (6 comma negative 3).

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).

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 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).

Explanation

For y = √(−x − 3), the radicand must be nonnegative, so −x − 3 ≥ 0, which gives x ≤ −3. The graph begins at (−3, 0) and extends to the left and upward. For example, at x = −7, y = √(7 − 3) = 2, matching the graph described in choice D.

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