Square Root and Absolute Value Functions — Test

Question 22 • Algebraic Reasoning

Which function has a range limited to only negative numbers?

Answer

Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 in increments of 2. A parabola opens up and passes through (negative 3 comma 1) and (negative 1 comma 1). Its vertex is at (negative 2 comma negative 3).

Image with description Coordinate plane with x-axis and y-axis. A decreasing curve begins at approximately negative 2 comma 1, crosses the x-axis near negative 1 comma 0, then continues downward while flattening as it moves to the right. The curve passes near 2 comma negative 1 and approaches 8 comma negative 2. An arrow on the right end indicates the graph continues indefinitely. The curve decreases throughout the visible domain, with the rate of decrease becoming smaller as x increases.

Image with description On a coordinate plane, the x-axis ranges from negative 8 to 8 by 2, and the y-axis ranges from negative 10 to 4 by 2. The graph has a draw-up in the shape of an inverted v with a vertex at (2 negative 1). One line passes through (0 comma negative 3) and extends infinitely into the third quadrant. The other line passes through (4 comma negative 3) and extends infinitely into the fourth quadrant.

Image with description Coordinate plane with x-axis and y-axis. A straight line with negative slope extends across the graph with arrows on both ends, indicating it continues indefinitely. The line passes through approximately negative 3 comma 0 and 0 comma negative 3, crossing the x-axis at negative 3 comma 0 and the y-axis at 0 comma negative 3. The graph decreases from left to right, moving from the upper-left quadrant to the lower-right quadrant.

Explanation

A function’s range is the set of its possible y-values. In choice C, the graph is an upside-down V with its highest point at y = −1, and both sides extend downward, so every y-value is −1 or less. Therefore, its range contains only negative numbers.

AI-written and checked against the verified answer.

More from this Course

Test

Test

Test