Practice Test

Question 2 • Algebra 2 with Probability

Which of the following could be the graph of y is equal to negative x to the n th power where n is odd?

Answer

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 6 to 6 by twos with grid lines every 1 unit. An S-shaped curve passes through the origin 0 comma 0, 1 comma 1, and negative 1 comma negative 1. The curve extends downward to the left, ending with an arrow near negative 2 comma negative 7, and extends upward to the right, ending with an arrow near 2 comma 7.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 6 to 6 by twos with grid lines every 1 unit. A U-shaped parabola opens downward with its vertex at 0 comma 0, passing through 1 comma negative 1 and negative 1 comma negative 1. The branches extend downward, ending with arrows near negative 2.6 comma negative 7 on the left and 2.6 comma negative 7 on the right.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 6 to 6 by twos with grid lines every 1 unit. A U-shaped parabola opens upward with its vertex at 0 comma 0, passing through 1 comma 1 and negative 1 comma 1. The branches extend upward, ending with arrows near negative 2.6 comma 7 on the left and 2.6 comma 7 on the right.

Image with description On a coordinate plane with x and y axes listed from negative 7 to 7 with an increment of 1, there is a curved graph. It passes through (negative 1 comma 1) (negative 2 comma 7), curves to the right and passes through the origin. It then curves to the left and passes through (1 comma negative 1) and (2 comma negative 7).

Explanation

For odd n, x^n has the same sign as x, so y = −x^n is positive when x is negative and negative when x is positive. The graph passes through the origin and falls from upper left to lower right; for example, it passes through (−1, 1) and (1, −1). Choice D shows this behavior, while the other choices either rise from left to right or are U-shaped.

AI-written and checked against the verified answer.

More from this Course

Practice Test

Practice Test

Practice Test