The Cubing Function — Quiz Answers

Graph the function f of x is equal to x cubed minus 4 x minus 1 Which are approximate solutions for x when f of x is equal to 0 ? Choose three correct answers.

A

negative 0 point 2 5

B

0 point 2 5

C

2 point 1 1

D

negative 2 point 1 1

E

negative 1 point 8 6

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Graph the function y is equal to x cubed plus 6 x squared plus 2 x minus 11 Based on the graph, what is the largest possible x -value if y is equal to 0 ? Round your answer to the nearest hundredth, if necessary.

A

1 point 1 1

B

13 point 2

C

5 point 2

D

1 point 9

3

Which statements correctly describe the graph of the function f of x is equal to x cubed minus 4 x squared minus 3 x plus 18 ? Choose three correct answers.

A

As x approaches negative infinity, y approaches positive infinity.

B

As x increases from negative infinity to positive infinity, the y -values increase, decrease, and then increase again.

C

There are three unique solutions to the function when y is equal to 0 .

D

The function has a double root.

E

The domain and range of the function are the set of real numbers.

4

The graph of the parent function f of x is equal to x cubed is transformed such that g⁡(x)=−2⁢x^3 How does the graph of g of x compare to the graph of f of x ?

A

g of x is stretched horizontally and reflected over the x -axis.

B

g of x is compressed horizontally and reflected over the line

C

g of x is compressed horizontally and reflected over the y -axis.

D

g of x is stretched horizontally and reflected over the y -axis.

5

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 graph has a positive y -intercept.

B

The domain of the function is all real numbers.

C

As x approaches negative infinity, y approaches negative infinity.

D

As the x -values increase, the y -values always increase.

E

The range of the function is y is greater than or equal to 20 .

6

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 decreases along the entire graph.

B

As x increases, y decreases, increases, and then decreases again.

C

As x increases, y increases along the entire graph.

D

As x increases, y increases, decreases, and then increases again.

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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 minus 4 cubed minus 7 The point 0 comma 0 on the graph of f of x corresponds to which point on the graph of g of x ?

A

4 comma 7

B

negative 4 comma 7

C

4 comma negative 7

D

negative 4 comma negative 7

8

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 5 cubed minus 6 The point 0 comma 0 on the graph of f of x corresponds to which point on the graph of g of x ?

A

negative 5 comma 6

B

5 comma negative 6

C

5 comma 6

D

negative 5 comma negative 6

9

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 decreases 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 increases along the entire graph.

10

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

negative 7 comma 9

C

9 comma negative 7

D

7 comma 9

11

Which statements correctly describe the graph of the function f of x is equal to x cubed minus 4 x squared minus 3 x plus 18 ? Choose three correct answers.

A

As x approaches negative infinity, y approaches positive infinity.

B

The domain and range of the function are the set of real numbers.

C

The function has a double root.

D

There are three unique solutions to the function when y is equal to 0 .

E

As x increases from negative infinity to positive infinity, the y -values increase, decrease, and then increase again.

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 On a coordinate plane, a curve goes through the point negative 1 comma negative 8. It increases to a relative maximum near 0 comma negative 3. Then it decreases to a relative minimum near 2 comma negative 10 and increases through the point 3 comma 0.

B

Image with description On a coordinate plane, a curve goes through the point negative 5 comma negative 6. It increases to a relative maximum near 4 comma 3. Then it decreases to a relative minimum near negative 2 comma negative 5 and increases through the point negative 1 comma 0.

C

Image with description On a coordinate plane, a curve goes through the point 1 comma negative 6. It increases to a relative maximum near 2 comma 3. Then it decreases to a relative minimum near 4 comma negative 5 and increases through the point 5 comma 0.

D

Image with description On a coordinate plane, a curve goes through the point negative 1 comma negative 6. It increases to a relative maximum near 0.3 comma 3. Then it decreases to a relative minimum near 2 comma negative 5 and increases through the point 3 comma 0.

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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 negative 7

B

7 comma 9

C

negative 7 comma 9

D

9 comma 7

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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 On a coordinate plane, a curve goes through the point negative 1 comma negative 6. It increases to a relative maximum near 0.3 comma 3. Then it decreases to a relative minimum near 2 comma negative 5 and increases through the point 3 comma 0.

B

Image with description On a coordinate plane, a curve goes through the point negative 1 comma negative 8. It increases to a relative maximum near 0 comma negative 3. Then it decreases to a relative minimum near 2 comma negative 10 and increases through the point 3 comma 0.

C

Image with description On a coordinate plane, a curve goes through the point 1 comma negative 6. It increases to a relative maximum near 2 comma 3. Then it decreases to a relative minimum near 4 comma negative 5 and increases through the point 5 comma 0.

D

Image with description On a coordinate plane, a curve goes through the point negative 5 comma negative 6. It increases to a relative maximum near 4 comma 3. Then it decreases to a relative minimum near negative 2 comma negative 5 and increases through the point negative 1 comma 0.

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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 graph has a positive y -intercept.

B

The range of the function is y is greater than or equal to 20 .

C

The domain of the function is all real numbers.

D

As the x -values increase, the y -values always increase.

E

As x approaches negative infinity, y approaches negative infinity.

16

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 On a coordinate plane, the graph of the parent cubic function is shifted 1 unit right and 2 units up.

B

Image with description On a coordinate plane, the graph of the parent cubic function is shifted 2 units left and 1 unit down.

C

Image with description On a coordinate plane, the graph of the parent cubic function is shifted 1 unit left and 2 units down.

D

Image with description On a coordinate plane, the graph of the parent cubic function is shifted 2 units right and 1 unit up.

17

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

A

Image with description On a coordinate plane, a curve goes through the point negative 4 comma negative 2. It increases to a relative maximum near negative 3 comma 2.3. Then it decreases to a relative minimum near negative 1.7 comma 2 and increases through the point negative 1 comma 6.

B

Image with description On a coordinate plane, a curve goes through the point negative 2 comma 2. It increases to a relative maximum near negative 1 comma 6.3. Then it decreases to a relative minimum near 0.3 comma 6 and increases through the point 1 comma 8.

C

Image with description On a coordinate plane, a curve goes through the point negative 2 comma negative 2. It increases to a relative maximum near negative 1 comma 2.3. Then it decreases to a relative minimum near 0.3 comma 2 and increases through the point 1 comma 6.

D

Image with description On a coordinate plane, a curve goes through the point negative 2 comma 0. It increases to a relative maximum near negative 1 comma 4.3. Then it decreases to a relative minimum near 0.3 comma 4 and increases through the point 1.5 comma 8.

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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 On a coordinate plane, a curve goes through the point negative 4 comma negative 8. It increases to a relative maximum near negative 2.5 comma negative 1.6. Then it decreases to a relative minimum near negative 1.4 comma negative 2.4,and increases through the point 0 comma 4.

B

Image with description On a coordinate plane, a curve goes through the point negative 6 comma negative 6. It intersects the x-axis at the point negative 5 comma 0 and increases to a relative maximum near negative 4.5 comma 0.4. Then it decreases to a relative minimum near negative 3.4 comma negative 0.4 and increases through the point negative 2 comma 6.

C

Image with description On a coordinate plane, a curve goes through the point negative 4 comma negative 4. It intersects the x-axis at the point negative 3.5 comma 0 and increases to a relative maximum near negative 2.5 comma 2.4. Then it decreases to a relative minimum near negative 1.4 comma 1.8 and increases through the point 0 comma 8.

D

Image with description On a coordinate plane, a curve goes through the point negative 4 comma negative 6. It intersects the x-axis at the point negative 3 comma 0 and increases to a relative maximum near negative 2.5 comma 0.4. Then it decreases to a relative minimum near negative 1.4 comma negative 0.4 and increases through the point 0 comma 6.

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