AnswersAlgebraic ReasoningCubic and Cube Root Functions

Cubic and Cube Root Functions — Test Answers

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1
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Which represents g of x , the translated function?

A
g of x is equal to x plus 6 cubed minus 4
B
g of x is equal to x minus 6 cubed minus 4
C
g of x is equal to x plus 4 cubed plus 6
D
g of x is equal to x minus 4 cubed plus 6
2
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Which equation represents f of x ?

A
f of x is equal to cube root of negative x
B
f of x is equal to negative cube root of x minus 1
C
f of x is equal to cube root of negative x minus 1
D
f of x is equal to negative cube root of x
3

Which statements correctly describe the graph of the function f of x is equal to x cubed minus 2 x squared minus 19 x plus 20 ? Choose three correct answers.

A
The range of the function is y is greater than or equal to 20 .
B
As x approaches negative infinity, y approaches negative infinity.
C
The domain of the function is all real numbers.
D
The graph has a positive y -intercept.
E
As the x -values increase, the y -values always increase.
4

Which is the graph of the cube root function f of x is equal to cube root of x ?

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 negative 2 at the lower left, increases gradually through the third quadrant, passes through the origin, and continues increasing through the first quadrant, ending with an arrow near the point 8 comma 2 at the upper right, forming an S-shaped curve with a gentle positive slope.
B
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 3 at the upper left, decreases gradually through the second quadrant, passes through approximately the point 0 comma 1 on the y-axis, and continues decreasing through the fourth quadrant, ending with an arrow near the point 8 comma negative 3 at the lower right, forming an S-shaped curve with a negative overall direction.
C
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.
D
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 negative 3 at the lower left, increases gradually through the third quadrant, passes through the origin, and continues increasing through the first quadrant, ending with an arrow near the point 4 comma 3 at the upper right, forming an S-shaped curve with a positive overall direction.
5

The graph of the parent function f of x is equal to x cubed is translated to form g of x is equal to x minus 7 cubed plus 9 The point 0 comma 0 on the graph of f of x corresponds to which point on the graph of g of x ?

A
9 comma 7
B
9 comma negative 7
C
7 comma 9
D
negative 7 comma 9
6

Which is the graph of the function f of x is equal to x cubed plus x squared plus 4 ?

A
Image with description A coordinate plane with a cubic curve. The horizontal axis and vertical axis are labeled from negative 8 to 8 in increments of 2. The curve starts in the third quadrant near the point negative 3 comma negative 8, rises through the point negative 2 comma negative 2, passes through the point negative 1 comma 2, and continues upward into the second quadrant, displaying a characteristic S-shape.
B
Image with description A coordinate plane with a cubic curve. The horizontal axis and vertical axis are labeled from negative 8 to 8 in increments of 2. The curve starts in the third quadrant near the point negative 1 comma negative 8, rises through the point negative 1 comma negative 2, passes through the point 0 comma 2, and continues upward into the first quadrant, displaying a characteristic S-shape.
C
Image with description " A coordinate plane with a cubic curve. The horizontal axis and vertical axis are labeled from negative 8 to 8 in increments of 2. The curve starts in the third quadrant near the point negative 2 comma negative 8, rises through the point negative 2 comma negative 4, passes through the point negative 1 comma 2, and continues upward into the second quadrant near the point 0 comma 6, displaying a characteristic S-shape."
D
Image with description " A coordinate plane with a cubic curve. The horizontal axis and vertical axis are labeled from negative 8 to 8 in increments of 2. The curve starts in the third quadrant near the point negative 2 comma negative 8, rises through the point negative 2 comma negative 4, passes through the point negative 1 comma 4, and continues upward into the second quadrant near the point negative 1 comma 8, displaying a characteristic S-shape."
7

Which is the graph of the function f of x is equal to x cubed plus x squared plus x plus 1 ?

A
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis. Both axes are labeled from negative 4 to 4. The curve begins in the third quadrant, with an arrowhead pointing downward near the coordinates negative 1 point 2 comma negative 4. Moving upward and to the right, the curve passes through the grid intersection at negative 1 comma negative 2. The curve crosses the vertical y-axis at the point 0 comma negative 1. From there, the curve turns upward more steeply, crossing the horizontal x-axis between 0 and 1, and passes through the grid intersection at 1 comma 2.
B
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis. Both axes are labeled from negative 4 to 4. The curve begins in the fourth quadrant with an arrowhead pointing downward near the coordinates 0 point 5 comma negative 4. Moving upward and to the right, the curve passes through the grid intersection at 1 comma negative 2. It then curves more gradually, flattened near the grid intersection at 2 comma negative 1. From there, the curve turns upward more steeply, crossing the horizontal x-axis between 2 and 3, and passes through the grid intersection at 3 comma 2. It continues upward into the first quadrant, ending with an arrowhead pointing upward near the coordinates 3 point 2 comma 4.
C
Image with description A coordinate plane displays the x-axis labeled from negative 4 to 4 in increments of 1 and the y-axis labeled from negative 4 to 4 in increments of 1. An increasing curve enters from below near 0.2 comma negative 4, rises steeply, passes through approximately 1 comma 0 and 2 comma 1.
D
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis. Both axes are labeled from negative 4 to 4. The curve begins in the fourth quadrant, with an arrowhead pointing downward near the coordinates negative 1 point 2 comma negative 4. Moving upward and to the right, the curve passes through the grid intersection at negative 1 comma negative 2. It then curves more gradually, crossing the horizontal x-axis between negative 1 and 0, and passes through the vertical y-axis at the point 0 comma 1. From there, the curve turns upward more steeply, passing through the grid intersection at 1 comma 4.
8

Which cube root function is always decreasing as x increases?

A
f of x is equal to cube root of x minus 8
B
f of x is equal to cube root of x minus 5
C
f of x is equal to negative cube root of x plus 5
D
f of x is equal to cube root of negative open paren 5 minus x close paren
9

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 ?

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. 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.
B
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.
C
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.
D
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.
10

The graph of the parent function f of x is equal to x cubed is translated to form the graph of g of x is equal to x plus 3 cubed minus 4 The point 0 comma 0 on the graph of f of x corresponds to which point on the graph of g of x ?

A
3 comma 4
B
3 comma negative 4
C
negative 3 comma 4
D
negative 3 comma negative 4
11

Which describes how to graph g of x is equal to cube root of x minus 5 plus 7 by transforming the parent function?

A
Translate the parent function 5 units to the right and 7 units up.
B
Translate the parent function 5 units up and 7 units to the right.
C
Translate the parent function 5 units to the left and 7 units up.
D
Translate the parent function 5 units down and 7 units to the right.
12

Which is the graph of the function f of x is equal to 2 x cubed minus 7 x squared plus 2 x plus 3 ?

A
Image with description A coordinate plane shows a cubic polynomial function. The x-axis is labeled from negative 8 to 8 in increments of 2, and the y-axis is labeled from negative 8 to 8 in increments of 2. The graph has a local maximum at the point 2 comma 3 and a local minimum at the point 4 comma negative 5. From the local maximum, the curve moves downwards and to the left, crossing the x-axis near 1 comma 0 and continuing downwards to an arrowhead pointing near 1 comma negative 7. From the local minimum, the curve moves upwards and to the right, crossing the x-axis near 5 comma 0 and continuing upwards to an arrowhead pointing near 5 comma 8.
B
Image with description A coordinate plane shows a cubic polynomial function. The x-axis is labeled from negative 8 to 8 in increments of 2, and the y-axis is labeled from negative 8 to 8 in increments of 2. The graph has a local maximum at the point negative 4 comma 3 and a local minimum at the point negative 2 comma negative 5. From the local maximum, the curve moves downwards and to the left, crossing the x-axis near negative 5 comma 0 and continuing downwards to an arrowhead pointing near negative 5 comma negative 7. From the local minimum, the curve moves upwards and to the right, crossing the x-axis near negative 1 comma 0 and continuing upwards to an arrowhead pointing near negative 1 comma 8.
C
Image with description A coordinate plane shows a cubic polynomial function. The x-axis is labeled from negative 8 to 8 in increments of 2, and the y-axis is labeled from negative 8 to 8 in increments of 2. The graph has a local maximum on the y-axis at the point 0 comma negative 1 and a local minimum at the point 2 comma negative 8. From the local maximum, the curve moves downwards and to the left, continuing downwards to an arrowhead pointing near negative 1 comma negative 8. From the local minimum, the curve moves upwards and to the right, crossing the x-axis near 3 comma 0 and continuing upwards to an arrowhead pointing near 4 comma 8.
D
Image with description A coordinate plane shows a cubic polynomial function. The x-axis is labeled from negative 8 to 8 in increments of 2, and the y-axis is labeled from negative 8 to 8 in increments of 2. The graph has a local maximum on the y-axis at the point 0 comma 3 and a local minimum at the point 2 comma negative 5. From the local maximum, the curve moves downwards and to the left, crossing the x-axis near negative 1 comma 0 and continuing downwards to an arrowhead pointing near negative 1 comma negative 7. From the local minimum, the curve moves upwards and to the right, crossing the x-axis near 3 comma 0 and continuing upwards to an arrowhead pointing near 3 comma 8.
13

What is the domain of f of x is equal to cube root of x ?

A
all integers
B
all real numbers
C
positive numbers and zero
D
whole numbers
14

Which is the graph of the function f of x is equal to x cubed plus 6 x squared plus 11 x plus 6 ?

A
Image with description A coordinate plane has both x and y axes labeled from negative 8 to 8. A curve is plotted that passes through the point negative 4 comma negative 4, intersects the x-axis at the point negative 3.5 comma 0, increases to a relative maximum near the point negative 2.5 comma 2.4, decreases to a relative minimum near the point negative 1.4 comma 1.8, and increases through the point 0 comma 8.
B
Image with description A coordinate plane has both x and y axes labeled from negative 8 to 8. A curve is plotted that passes through the point negative 4 comma negative 6, intersects the x-axis at the point negative 3 comma 0, increases to a relative maximum near the point negative 2.5 comma 0.4, decreases to a relative minimum near the point negative 1.4 comma negative 0.4, and increases through the point 0 comma 6.
C
Image with description A coordinate plane has both x and y axes labeled from negative 8 to 8. A curve is plotted that passes through the point negative 6 comma negative 6, intersects the x-axis at the point negative 5 comma 0, increases to a relative maximum near the point negative 4.5 comma 0.4, decreases to a relative minimum near the point negative 3.4 comma negative 0.4, and increases through the point negative 2 comma 6.
D
Image with description A coordinate plane has both x and y axes labeled from negative 8 to 8. A curve is plotted that passes through the point negative 4 comma negative 8, increases to a relative maximum near the point negative 2.5 comma negative 1.6, decreases to a relative minimum near the point negative 1.4 comma negative 2.4, and increases through the point 0 comma 4.
15

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 ?

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.
16

Which is the graph of y is equal to cube root of x plus 1 minus 2 ?

A
Image with description A coordinate plane with an S-shaped 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. The curve extends from the lower-left area of the plane, where an arrow at approximately negative 9 comma negative 4 points to the left. The curve rises with an increasing positive slope, passing through the center of the plane near x equals 4, then levels off with a decreasing positive slope as it continues to the right, ending with an arrow at approximately 9 comma 0 pointing to the right near the x-axis.
B
Image with description A coordinate plane with an S-shaped 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. The curve extends from the lower-left area of the plane, where an arrow at approximately negative 9 comma negative 4 points to the left. The curve rises with an increasing positive slope, passing through the center of the plane near x equals 2 and y equals 0, then levels off with a decreasing positive slope as it extends toward the upper-right, ending with an arrow at approximately 9 comma 0 pointing to the right slightly above the x-axis.
C
Image with description A coordinate plane with an S-shaped 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. The curve extends from the lower-left area of the plane, where an arrow at approximately negative 7 comma 0 points to the left just below the x-axis. The curve rises with an increasing positive slope through the center-left area of the plane, passing through approximately negative 2 comma 1, then levels off with a decreasing positive slope as it continues to the upper-right, ending with an arrow at approximately 9 comma 4 pointing to the right.
D
Image with description A coordinate plane with an S-shaped 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. The curve extends from the lower-left area of the plane, where an arrow at approximately negative 9 comma negative 1 points to the left. The curve rises with an increasing positive slope through the center of the plane, passing through the origin area, then levels off with a decreasing positive slope as it extends toward the upper-right, ending with an arrow at approximately 8 comma 4 pointing to the right.
17

Which statement is true of the function f of x is equal to negative cube root of x ? Choose three correct answers.

A
The function is always increasing.
B
The function has a range of start set y such that negative infinity is less than y comma y is less than infinity end set .
C
The function has a domain of all real numbers.
D
The function is a reflection of y is equal to cube root of x .
E
The function passes through the point 3 comma negative 27 .
19

Which best describes the graph of the cubic function f of x is equal to x cubed plus x squared plus x plus 1 ?

A
As x increases, y increases along the entire graph.
B
As x increases, y increases, decreases, and then increases again.
C
As x increases, y decreases, increases, and then decreases again.
D
As x increases, y decreases along the entire graph.
20

The graph of the parent function f of x is equal to x cubed is translated to form the graph of g of x is equal to open paren x minus 1 close paren cubed plus 2 Which is the graph of g of x , the translated function?

A
Image with description A coordinate plane with an S-shaped curve. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve extends from the upper portion of the plane near x equals 0 and y equals 4, descending steeply with a negative slope through the center of the plane near the origin, and continuing downward with a decreasing negative slope. The upper end of the curve ends with an arrow pointing upward near 0 comma 4 and the lower end ends with an arrow pointing downward near negative 2 comma negative 5.
B
Image with description A coordinate plane with an S-shaped curve. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve extends from the upper-center area of the plane near negative 2 comma 4 and descends with a steep negative slope through the center-left area of the plane, continuing downward with a decreasing negative slope toward the lower portion of the plane. The upper end of the curve ends near negative 2 comma 4 and the lower end ends with an arrow pointing downward near negative 3 comma negative 5.
C
Image with description A coordinate plane with an S-shaped curve. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve extends from the lower portion of the plane near negative 1 comma negative 5 and rises steeply with a positive slope through the center area near the y-axis, continuing upward with a decreasing positive slope toward the upper-right area near 1 comma 4. The lower end ends with an arrow pointing downward near negative 1 comma negative 5 and the upper end ends with an arrow pointing upward near 1 comma 4.
D
Image with description A coordinate plane with an S-shaped curve. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The curve extends from the lower-right area of the plane near 0 comma negative 5 and rises steeply with a positive slope through the center-right area of the plane, continuing upward with a decreasing positive slope toward the upper-right area near 4 comma 5. The lower end ends with an arrow pointing downward near 0 comma negative 5 and the upper end ends with an arrow pointing upward near 4 comma 5.
21

Which equation represents g of x ?

A
g of x is equal to cube root of x minus 4
B
g of x is equal to cube root of x minus 1 point 5
C
g of x is equal to cube root of x plus 4
D
g of x is equal to cube root of x plus 1 point 5

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