Deck 3: Polynomial and Rational Functions

Question 1

Use transformations of the graph o to graph the function.

Answer 1

D

Question 2

Use transformations of the graph o to graph the function.

Answer 2

A

Question 3

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

Answer 3

D

Question 4

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

A) Yes; degree 1
B) No; x is a negative term
C) No; it is a ratio
D) Yes; degree 4

Question 5

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

Question 6

Use transformations of the graph o to graph the function.

Question 7

Use transformations of the graph o to graph the function.

Question 8

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

Question 9

Use transformations of the graph o to graph the function.

Question 10

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

A) Yes; degree 0
B) Yes; degree 6
C) Yes; degree 1
D) No; x is raised to a negative power

Question 11

Use transformations of the graph o to graph the function.

Question 12

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

Question 13

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

A) Yes; degree 7
B) Yes; degree 1
C) Yes; degree 3
D) Yes; degree 5

Question 14

Use transformations of the graph o to graph the function.

Question 15

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

A) Yes; degree 6
B) Yes; degree 5
C) Yes; degree 3
D) No; the last term has no variable

Question 16

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

Question 17

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

A) Yes; degree 0
B) Yes; degree 5
C) No; x has a fractional coefficient
D) Yes; degree 1

Question 18

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

Question 19

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

Question 20

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) = 5

A) No; it is a constant
B) Yes; degree 0
C) Yes; degree 1
D) No; it contains no variables

Question 21

Use transformations of the graph o to graph the function.

Question 22

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 23

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Question 24

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 25

Use transformations of the graph o to graph the function.

Question 26

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Question 27

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Question 28

Use transformations of the graph o to graph the function.

Question 29

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Question 30

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Question 31

Use transformations of the graph o to graph the function.

Question 32

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 33

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 34

Use transformations of the graph o to graph the function.

Question 35

Use transformations of the graph o to graph the function.

Question 36

Use transformations of the graph o to graph the function.

Question 37

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Question 38

Use transformations of the graph o to graph the function.

Question 39

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Question 40

Use transformations of the graph o to graph the function.

Question 41

Find the power function that the graph of f resembles for large values of |x|.

Question 42

Find the x- and y-intercepts of f.

Question 43

Find the power function that the graph of f resembles for large values of |x|.

Question 44

Find the x- and y-intercepts of f.

Question 45

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 46

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 47

Find the x- and y-intercepts of f.

Question 48

Find the x- and y-intercepts of f.

Question 49

Find the x- and y-intercepts of f.

Question 50

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 51

Find the power function that the graph of f resembles for large values of |x|.

Question 52

Find the x- and y-intercepts of f.

Question 53

Find the x- and y-intercepts of f.

Question 54

Find the x- and y-intercepts of f.

Question 55

Find the x- and y-intercepts of f.

Question 56

Find the x- and y-intercepts of f.

Question 57

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 58

Find the power function that the graph of f resembles for large values of |x|.

Question 59

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

Question 60

Find the power function that the graph of f resembles for large values of |x|.

Question 61

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 62

Write the word or phrase that best completes each statement or answers the question.
The amount of water (in gallons) in a leaky bathtub is given in the table below. Using a graphing utility, fit the data to a third degree polynomial (or a cubic). Then approximate the time at which there is maximum amount
Of water in the tub, and estimate the time when the water runs out of the tub. Express all your answers rounded
To two decimal places.

A) maximum amount of water after 5.37 minutes; water runs out after 11.06 minutes
B) maximum amount of water after 8.23 minutes; water runs out after 19.73 minutes
C) maximum amount of water after 5.31 minutes; water runs out after 8.23 minutes
D) maximum amount of water after 5.31 minutes; water never runs out

Question 63

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

Question 64

Choose the one alternative that best completes the statement or answers the question.

Question 65

Write the word or phrase that best completes each statement or answers the question.
The profits (in millions) for a company for 8 years was as follows: Find the cubic function of best fit to the data.

Question 66

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 67

Determine the maximum number of turning points of f.

Question 68

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 69

Use the Factor Theorem to determine whether x - c is a factor of f(x).

A) Yes
B) No

Question 70

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 71

Determine the maximum number of turning points of f.

A) 2
B) 3
C) 4
D) 1

Question 72

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

Question 73

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 74

Determine the maximum number of turning points of f.

A) 3
B) 2
C) 4
D) 1

Question 75

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 76

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 77

Use the Factor Theorem to determine whether x - c is a factor of f(x).

A) Yes
B) No

Question 78

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

Question 79

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

Question 80

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.