AnswersAlgebraic ReasoningCubic and Cube Root Functions — TestQuestion 15
15
QuizMultiple Choice

Cubic and Cube Root Functions — Test

Question 15 • Algebraic Reasoning

The function f of x is equal to cube root of x is reflected over the x -axis to create the graph of g of x is equal to negative cube root of x Which is the graph of g of x ?

Answer
A
Image with description A coordinate plane with a curve. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 5 to 5 in increments of 1. A curve begins with an arrow near the point negative 10 comma 2 at the left, decreases gradually through the second quadrant, passes through the origin, and continues decreasing through the fourth quadrant, ending with an arrow near the point 10 comma negative 3 at the lower right, forming an S-shaped curve with a negative overall direction.
B
Image with description A coordinate plane with the x-axis labeled from negative 10 to 10 and the y-axis labeled from negative 5 to 5. A cube root function is plotted that passes through the point negative 8 comma negative 2, has an inflection point at the point 0 comma 0, and passes through the point 8 comma 2.
C
Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 and the y-axis labeled from negative 10 to 10. A cube root function is plotted that passes through the point negative 2 comma 8, has an inflection point at the point 0 comma 0, and passes through the point 2 comma negative 8.
D
Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 and the y-axis labeled from negative 10 to 10. A cube root function is plotted that passes through the point negative 2 comma negative 8, has an inflection point at the point 0 comma 0, and passes through the point 2 comma 8.

Explanation

Reflecting a graph over the x-axis changes each point (x, y) to (x, −y). Since f(x) = ∛x increases from left to right, g(x) = −∛x decreases from left to right and passes through the origin. Choice A shows that decreasing S-shaped curve; the other choices show increasing curves or a different relationship between x and y.

AI-written and checked against the verified answer.

Previous
Next

More from this Course

Quiz
25 verified answers

Test

Quiz
25 verified answers

Test

Quiz
25 verified answers

Test