Practice Test

Question 6 • Algebra II

Which graph represents y is equal to cube root of x plus 2 ?

Answer

image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 8 to 8 by twos with grid lines every 1 unit. An S-shaped curve crosses the vertical axis at 0 comma negative 2 and crosses the horizontal axis at 8 comma 0. The curve extends to the left ending in an arrow near negative 9 comma negative 4, and extends to the right ending in an arrow near 9 comma 0.3. - incorrect

image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 8 to 8 by twos with grid lines every 1 unit. An S-shaped curve crosses the horizontal axis at negative 2 comma 0 and crosses the vertical axis near 0 comma 1.3. The curve extends to the left ending in an arrow near negative 9 comma negative 1.5, and extends to the right ending in an arrow near 9 comma 2.2. - no response given

image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. A graph of cubic function passes through points (negative 8 comma 0), (0 comma 2), and (8 comma 4). The curve has a point of inflection at (0 comma 2). - not selected, this is the correct answer

image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 8 to 8 by twos with grid lines every 1 unit. An S-shaped curve crosses the horizontal axis at 2 comma 0 and crosses the vertical axis near 0 comma negative 1.3. The curve extends to the left ending in an arrow near negative 9 comma negative 2.2, and extends to the right ending in an arrow near 9 comma 2. - no response given

Explanation

For y = ∛x + 2, start with the cube-root graph y = ∛x and shift it up 2 units. For example, x = −8 gives y = 0, x = 0 gives y = 2, and x = 8 gives y = 4. Choice C passes through those points and has its center/inflection point at (0, 2), so it represents the function.

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