Deck 6: Higher-Degree Polynomial and Rational Functions

Question 1

Determine whether the polynomial function is cubic or quartic.

A) Cubic
B) Quartic

Answer 1

A

Question 2

Use the given graph of the polynomial function to estimate the x-intercepts.

A) $- 3 , - 1,2$
В) $- 3 , - 1,2$
C) $- 3 , - 1,0,2$
D) $- 1,0,2$

Answer 2

C

Question 3

$f ( x ) = 0.62 x ^ { 3 } - 5 x ^ { 2 } + 11 x + 8$

A) [-10,5] by [-300,300]
B) [-30,80] by [-8000,4000]
C) [-10,10] by [-10,10]
D) [-5,10] by [-100,300]

Answer 3

B

Question 4

Determine whether the polynomial function is cubic or quartic.

A) Cubic
B) Quartic

Question 5

$f ( x ) = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$

A) [-3,3] by [-3,4]
B) [-2,2] by [-10,-5]
C) [-3,3] by [-10,5]
D) [-5,5] by [-2,1]

Question 6

$f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - x ^ { 3 } - 10 x ^ { 2 } + 3 x + 10$

A) [-10,10] by [-10,10]
B) [-6,6] by [-10,200]
C) [-10,10] by [-100,100]
D) [-3,3] by [-10,30]

Question 7

$f ( x ) = 0.3 x ^ { 5 } + 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } + 2$

A) [-5000,5000] by [-150,150]
B) [-10,10] by [-1200,2000]
C) [-6,6] by [-3000,3000]
D) [-20,20] by [-5000,8000]

Question 8

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and
whether the polynomial function is cubic or quartic.

A) Positive; Cubic
B) Negative; Quartic
C) Positive; Quartic
D) Negative; Cubic

Question 9

Determine whether the polynomial function is cubic or quartic.

A) Quartic
B) Cubic

Question 10

Use the given graph of the polynomial function to estimate the x-intercepts.

A) $- 9,3$
B) $- 9 , - 1$
C) $- 1,3$
D) $- 9 , - 1,3$

Question 11

Match the polynomial function with the graph.

Question 12

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and
whether the polynomial function is cubic or quartic.

A) Negative; Cubic
B) Positive; Cubic
C) Negative; Quartic
D) Positive; Quartic

Question 13

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and
whether the polynomial function is cubic or quartic.

A) Negative; Quartic
B) Positive; Cubic
C) Negative; Cubic
D) Positive; Quartic

Question 14

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and
whether the polynomial function is cubic or quartic.

A) Negative; Cubic
B) Negative; Quartic
C) Positive; Quartic
D) Positive; Cubic

Question 15

Use the given graph of the polynomial function to estimate the x-intercepts.

A) $- 2,1$
B) $- 2,3$
C) $- 2,1,3$
D) $- 3,1,2$

Question 16

$f ( x ) = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47$

A) [-5,5] by [-500,100]
B) [-8,10] by [-100,300]
C) [-3,10] by [-400,100]
D) [-10,10] by [-150,150]

Question 17

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and
whether the polynomial function is cubic or quartic.

A) Positive; Quartic
B) Negative; Cubic
C) Positive; Cubic
D) Negative; Quartic

Question 18

$f ( x ) = 4.5 x ^ { 3 } + 12 x ^ { 2 } - 82$

A) [-2,8] by [-250,150]
B) [-5,5] by [-200,50]
C) [-100,100] by [-10,10]
D) [-6,6] by [-50,100]

Question 19

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and
whether the polynomial function is cubic or quartic.

A) Positive; Cubic
B) Negative; Cubic
C) Negative; Quartic
D) Positive; Quartic

Question 20

Determine whether the polynomial function is cubic or quartic.

A) Quartic
B) Cubic

Question 21

State the degree and leading coefficient of the polynomial function.

Question 22

State the degree and leading coefficient of the polynomial function.

Question 23

Predict the end behavior of the graph of the function.

A) Up on left side, down on right side
B) Down on left side, up on right side
C) Up on both sides
D) Down on both sides

Question 24

Match the polynomial function with the graph.

Question 25

Match the polynomial function with the graph.

Question 26

State the degree and leading coefficient of the polynomial function.

A) Degree: 6; leading coefficient: 16
B) Degree: 5; leading coefficient: 16
C) Degree: 16; leading coefficient: 4
D) Degree: 4; leading coefficient: 16

Question 27

State the degree and leading coefficient of the polynomial function.

Question 28

State the degree and leading coefficient of the polynomial function.

Question 29

Determine a window that will provide a comprehensive graph of the polynomial function.

Question 30

State the degree and leading coefficient of the polynomial function.

A) Degree: 14; leading coefficient: 4
B) Degree: 8; leading coefficient: 14
C) Degree: 7; leading coefficient: 14
D) Degree: 4; leading coefficient: 14

Question 31

Match the polynomial function with the graph.

Question 32

Predict the end behavior of the graph of the function.

A) Down on both sides
B) Up on the right side, down on the left side
C) Up on both sides
D) Down on the right side, up on the left side

Question 33

Choose the graph that satisfies the given conditions.
Polynomial of degree 3 with three distinct x nd a positive leading coefficient

Question 34

Match the polynomial function with the graph.

Question 35

Predict the end behavior of the graph of the function.

A) Down on both sides
B) Up on both sides
C) Down on the right side, up on the left side
D) Up on the right side, down on the left side

Question 36

Predict the end behavior of the graph of the function.

A) Down on both sides
B) Up on left side, down on right side
C) Down on left side, up on right side
D) Up on both sides

Question 37

Match the polynomial function with the graph.

Question 38

Determine a window that will provide a comprehensive graph of the polynomial function.

Question 39

Predict the end behavior of the graph of the function.

A) Down on left side, up on right side
B) Up on left side, down on right side
C) Down on both sides
D) Up on both sides

Question 40

State the degree and leading coefficient of the polynomial function.

Question 41

Choose the graph that satisfies the given conditions.
Degree 4 with four x s and a negative leading coefficient

Question 42

Find the cubic or quartic function that models the data in the table.

Question 43

Find the cubic or quartic function that models the data in the table.

- $$\begin{array} { c | c c c c c } \mathrm { x } & 2 & 3 & 5 & 6 & 7 \\\hline \mathrm { y } & 3 & 5 & 9 & 15 & 19\end{array} \text { (Quartic) }$$

A) $y = - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } - 20.02 x ^ { 2 } + 51.93 x - 44.00$
B) $y = 0.16 x ^ { 4 } + 3.77 x ^ { 3 } + 20.02 x ^ { 2 } + 51.93 x - 44.00$
C) $y = - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } + 20.02 x ^ { 2 } + 55.93 x - 46.00$
D) $y = - 0.18 x ^ { 4 } + 3.77 x ^ { 3 } - 20.02 x ^ { 2 } + 41.93 x - 44.00$

Question 44

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.

Question 45

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.
The polynomial measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase between 12 and 13 seconds?

A) No
B) Yes

Question 46

5 is an approximation of the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number of hundred thousands of tires that must be sold to maximize
Profit.

A) 5.5 hundred thousand
B) 5 hundred thousand
C) 4 hundred thousand
D) 4.5 hundred thousand

Question 47

Find the cubic or quartic function that models the data in the table.

Question 48

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.
The following polynomial approximates the rabbit population in a particular area, R(x) = -0.135x5 + 2.952x4 + 3500, where x is the number of years from 1995. Use a graphing calculator to
Describe the rabbit population from the years 1995 to 2010.

A) The population decreases.
B) The population remains stable.
C) The population increases.

Question 49

Suppose that the population of a certain city during a certain time period can be approximated by , where x is time in years since 2010. By sketching a graph of P(x), estimate during what time period the population of the city would be increasing.

A) Between 2010 and 2024
B) Between 2015 and 2045
C) Between 2015 and 2038
D) Between 2010 and 2038

Question 50

Ariel, a marine biologist, models a population P of crabs, t days after being left to reproduce, with the function . Assuming that this model continues to be accurate, when will this population become extinct? (Round to the nearest day.)

A) 707 days
B) 911 days
C) 1512 days
D) 547 days

Question 51

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.
The polynomial approximates the shark population in a particular area, where x is the number of years from 1985. Use a graphing calculator to describe the shark population from the years
1985 to 2010.

A) The population decreases.
B) The population increases.
C) The population remains stable.

Question 52

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.

Question 53

Choose the graph that satisfies the given conditions.
Polynomial of degree 4 with two distinc s and a negative leading coefficient

Question 54

Choose the graph that satisfies the given conditions.
Quartic polynomial with one x intercept and a positive leading coefficient

Question 55

Find the cubic or quartic function that models the data in the table.

Question 56

Find the cubic or quartic function that models the data in the table.

Question 57

Find the cubic or quartic function that models the data in the table.

Question 58

A population of birds in a small county can be modeled by the polynomial where x=1 corresponds to July 1, x=2 to July 2 , and so on. On what day does f estimate the population to be 8550 ?

A) July 13 th
B) July 12 th
C) July 11 th
D) July 14th

Question 59

Choose the graph that satisfies the given conditions.
Degree 3 with one x intercept and a positive leading coefficient

Question 60

0 is an approximation of the number of salmon swimming upstream to spawn, where x represents the water temperature in degrees Celsius. Find the temperature that produces the
Maximum number of salmon.

Question 61

Solve the polynomial equation.

Question 62

A) 1,-1,7
B)
C) 2,-2,7
D)

Question 63

The table shows the number of dollars spent in Country X (in millions) on environmental protection programs during the years 2000(x=1) through 2010(x=11) . Find the cubic model that is the best fit for this data. Round coefficients to three decimal places.

A)
B)
C)
D)

Question 64

Solve the polynomial equation by factoring.

Question 65

Solve the polynomial equation by factoring.

Question 66

The table below gives the violent crime rate (per 100,000 people) for a particular state every five years from 1970 to 2010. Use technology to find the cubic function that is the best fit for this data, where x is the number of years after 1970. Round to five decimal places.

Question 67

A) 6,-6
B) 9,-9
C) 3,-3
D) 18,-18

Question 68

Solve the polynomial equation by factoring.

Question 69

The table below gives the number of births, in thousands, to females over the age of 35 for a particular state every two years from 1994 to 2010. Use technology to find the quartic function that is the best fit for this data, where x is the number of years after 1994.
Round to five decimal places.

Question 70

Solve the polynomial equation.

Question 71

Find the cubic or quartic function that models the data in the table.

Question 72

The table below gives the violent crime rate (per 100,000 people) for a particular state every five years from 1970 to 2010. Use technology to find the cubic function that is the best fit for this data, where x is the number of years after 1970. Use the model to estimate the violent crime rate for the year 2014.

A) 11.6
B) 11.4
C) 11.8
D) 11

Question 73

Solve the polynomial equation by factoring.

Question 74

Solve the polynomial equation.

Question 75

Solve the polynomial equation by factoring.

Question 76

The table below gives the number of births, in thousands, to females over the age of 35 for a particular state every two years from 1994 to 2010. Use technology to find the quartic function that is the best fit for this data, where x is the number of years after 1994.
According to the model, how many births were there to females over the age of 35 in this state in 2014?

A) 106,368
B) 108,868
C) 94,368
D) 101,318

Question 77

The table below gives the number of births, in thousands, to females over the age of 35 for a particular state every two years from 1994 to 2010. Use technology to find the quartic function that is the best fit for this data, where x is the number of years after 1994.
According to the model, when will the number of births to females over the age of 35 first reach 80,000?

A) 2015
B) 2014
C) 2016
D) 2013

Question 78

The table below gives the violent crime rate (per 100,000 people) for a particular state every five years from 1970 to 2010. Use technology to find the cubic function that is the best fit for this data, where x is the number of years after 1970. Use the model to estimate the year having a violent crime rate of 11.4 per 100,000.

A) 2012
B) 2016
C) 2011
D) 2014

Question 79

Solve the polynomial equation by factoring.

Question 80

A)
B)
C)
D)