The Cube Root Function — Quiz

Question 3 • Algebra 2 with Probability

The graph of y is equal to cube root of x is reflected over the y -axis and then translated down 2 units to form f of x Which is the graph of f of x ?

Answer

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. An S-shaped curve decreases from left to right, intersecting the y-axis near the point 0 comma negative 2, intersecting the x-axis at the point negative 6 comma 0, and passing through the points negative 10 comma 0 point 2 6 and 6 comma negative 4.

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. An S-shaped curve increases from left to right, intersecting the y-axis near the point 0 comma 2, passing through the points negative 8 comma 0 and 6 comma 4, and flattened near the point negative 10 comma negative 0 point 2 6.

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. An S-shaped curve increases from left to right, intersecting the y-axis near the point 0 comma 1 point 2 6, intersecting the x-axis at the point negative 2 comma 0, and passing through the points negative 10 comma negative 2 and 6 comma 2.

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. An S-shaped curve decreases from left to right, intersecting the y-axis near the point 0 comma 1 point 2 6, intersecting the x-axis at the point 2 comma 0, and passing through the points negative 6 comma 2 and 10 comma negative 2.

Explanation

Reflecting y = ∛x across the y-axis replaces x with −x, giving y = ∛(−x) = −∛x. Translating down 2 units gives f(x) = −∛x − 2, a decreasing curve with y-intercept (0, −2) and x-intercept (−8, 0). Choice A is the graph with the curve decreasing and crossing the y-axis at −2.

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