Comparing Characteristics of Functions — Quiz

Question 67 • Mathematics II

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 by 2. A straight line with a negative slope passes through (negative 3 comma 0) and (0 comma negative 3). It extends infinitely in both directions.

Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 by 2. The graph has a smooth curve that starts from (negative 2 comma 1), goes down into the fourth quadrant, and passes through (7 comma negative 2).

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 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).

Explanation

A function’s range is the set of its possible y-values. In choice D, the inverted V has its highest point at y = −1, and both arms extend downward from there, so every y-value is at most −1 and therefore negative. The other graphs include at least one nonnegative y-value or extend to positive y-values.

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