College Algebra: Graphs and Models

Marvin L. Bittinger, Judith A.Beecher

Chapter 4

Polynomial Functions and Rational Functions - all with Video Answers

Educators

Section 1

Polynomial Functions and Modeling

Problem 1

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.
$$g(x)=\frac{1}{2} x^{3}-10 x+8$$

AG

Ankit Gupta

Numerade Educator

Problem 2

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$f(x)=15 x^{2}-10+0.11 x^{4}-7 x^{3}$$

AG

Ankit Gupta

Numerade Educator

Problem 3

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$h(x)=0.9 x-0.13$$

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Ankit Gupta

Numerade Educator

Problem 4

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$f(x)=-6$$

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Ankit Gupta

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Problem 5

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$g(x)=305 x^{4}+4021$$

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Ankit Gupta

Numerade Educator

Problem 6

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$h(x)=2.4 x^{3}+5 x^{2}-x+\frac{7}{8}$$

AG

Ankit Gupta

Numerade Educator

Problem 7

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$h(x)=-5 x^{2}+7 x^{3}+x^{4}$$

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Ankit Gupta

Numerade Educator

Problem 8

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$f(x)=2-x^{2}$$

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Problem 9

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$g(x)=4 x^{3}-\frac{1}{2} x^{2}+8$$

AG

Ankit Gupta

Numerade Educator

Problem 10

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic.

$$f(x)=12+x$$

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Ankit Gupta

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Problem 11

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)
$$f(x)=-3 x^{3}-x+4$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 12

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)

$$f(x)=\frac{1}{4} x^{4}+\frac{1}{2} x^{3}-6 x^{2}+x-5$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 13

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)

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

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 14

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)

$$f(x)=\frac{2}{5} x^{5}-2 x^{4}+x^{3}-\frac{1}{2} x+3$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 15

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)

$$f(x)=-3.5 x^{4}+x^{6}+0.1 x^{7}$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 16

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)

$$f(x)=-x^{3}+x^{5}-0.5 x^{6}$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 17

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)

$$f(x)=10+\frac{1}{10} x^{4}-\frac{2}{5} x^{3}$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 18

Select one of the four sketches $(a)-(d),$ which follow, to describe the end behavior of the graph of the function.
SKETCH CAN'T COPY)

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

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 19

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.
$$f(x)=-x^{6}+2 x^{5}-7 x^{2}$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 20

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.

$$f(x)=2 x^{4}-x^{2}+1$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 21

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.

$$f(x)=x^{5}+\frac{1}{10} x-3$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 22

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.

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

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 23

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.

Use substitution to determine whether $4,5,$ and
$-2$ are zeros of
$$f(x)=x^{3}-9 x^{2}+14 x+24$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 24

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.

Use substitution to determine whether $2,3,$ and
$-1$ are zeros of
$$f(x)=2 x^{3}-3 x^{2}+x+6$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 25

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.

Use substitution to determine whether $2,3,$ and
$-1$ are zeros of
$$g(x)=x^{4}-6 x^{3}+8 x^{2}+6 x-9$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 26

Use the leading-term test to match the function with one of the graphs (a)-(d), which follow.

Use substitution to determine whether $1,-2$ and 3 are zeros of
$$g(x)=x^{4}-x^{3}-3 x^{2}+5 x-2$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 27

Find the zeros of the polynomial function and state the multiplicity of each.
$$f(x)=(x+3)^{2}(x-1)$$

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Ankit Gupta

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Problem 28

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=(x+5)^{3}(x-4)(x+1)^{2}$$

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Ankit Gupta

Numerade Educator

Problem 29

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=-2(x-4)(x-4)(x-4)(x+6)$$

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Ankit Gupta

Numerade Educator

Problem 30

Find the zeros of the polynomial function and state the multiplicity of each.
$$f(x)=\left(x+\frac{1}{2}\right)(x+7)(x+7)(x+5)$$

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Ankit Gupta

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Problem 31

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=\left(x^{2}-9\right)^{3}$$

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Ankit Gupta

Numerade Educator

Problem 32

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=\left(x^{2}-4\right)^{2}$$

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Ankit Gupta

Numerade Educator

Problem 33

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=x^{3}(x-1)^{2}(x+4)$$

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Ankit Gupta

Numerade Educator

Problem 34

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=x^{2}(x+3)^{2}(x-4)(x+1)^{4}$$

AG

Ankit Gupta

Numerade Educator

Problem 35

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=-8(x-3)^{2}(x+4)^{3} x^{4}$$

AG

Ankit Gupta

Numerade Educator

Problem 36

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=\left(x^{2}-5 x+6\right)^{2}$$

AG

Ankit Gupta

Numerade Educator

Problem 37

Find the zeros of the polynomial function and state the multiplicity of each.

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

AG

Ankit Gupta

Numerade Educator

Problem 38

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=x^{4}-10 x^{2}+9$$

AG

Ankit Gupta

Numerade Educator

Problem 39

Find the zeros of the polynomial function and state the multiplicity of each.

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

AG

Ankit Gupta

Numerade Educator

Problem 40

Find the zeros of the polynomial function and state the multiplicity of each.

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

AG

Ankit Gupta

Numerade Educator

Problem 41

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=2 x^{3}-x^{2}-8 x+4$$

AG

Ankit Gupta

Numerade Educator

Problem 42

Find the zeros of the polynomial function and state the multiplicity of each.

$$f(x)=3 x^{3}+x^{2}-48 x-16$$

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Ankit Gupta

Numerade Educator

Problem 43

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.
$$f(x)=x^{3}-3 x-1$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 44

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.

$$f(x)=x^{3}+3 x^{2}-9 x-13$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 45

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.

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

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 46

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.

$$f(x)=x^{4}-2 x^{3}-5.6$$

Darshan Maheshwari

Darshan Maheshwari

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Problem 47

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.

$$f(x)=x^{3}-x$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 48

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.

$$f(x)=2 x^{3}-x^{2}-14 x-10$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 50

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.

$$f(x)=x^{8}+8 x^{7}-28 x^{6}-56 x^{5}+70 x^{4}$
$+56 x^{3}-28 x^{2}-8 x+1$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 51

Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places.

$$f(x)=x^{6}-10 x^{5}+13 x^{3}-4 x^{2}-5$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 51

Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function.
$$g(x)=x^{3}-1.2 x+1$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 52

Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function.

$$h(x)=-\frac{1}{2} x^{4}+3 x^{3}-5 x^{2}+3 x+6$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 53

Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function.

$$f(x)=x^{6}-3.8$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 54

Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function.

$$h(x)=2 x^{3}-x^{4}+20$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 55

Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function.

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

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 56

Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function.

$$f(x)=2 x^{4}-5.6 x^{2}+10$$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 57

Determine whether the statement is true or false.

If $P(x)=(x-3)^{4}(x+1)^{3},$ then the graph of the polynomial function $y=P(x)$ crosses the $x$ -axis at $(3,0)$

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Ankit Gupta

Numerade Educator

Problem 58

Determine whether the statement is true or false.

If $P(x)=(x+2)^{2}\left(x-\frac{1}{4}\right)^{5},$ then the graph of the polynomial function $y=P(x)$ crosses the $x$ -axis at $\left(\frac{1}{4}, 0\right)$

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Ankit Gupta

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Problem 59

Determine whether the statement is true or false.

If $P(x)=(x-2)^{3}(x+5)^{6},$ then the graph of $y=P(x)$ is tangent to the $x$ -axis at $(-5,0)$

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Ankit Gupta

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Problem 60

Determine whether the statement is true or false.

If $P(x)=(x+4)^{2}(x-1)^{2},$ then the graph of $y=P(x)$ is tangent to the $x$ -axis at $(4,0)$

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Ankit Gupta

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Problem 61

As a result of a greater number of births to older women and the increased use of fertility drugs, the number of twin births in the United States increased approximately $42 \%$ from 1990 to 2005 (Source: National Center for Health Statistics, U.S. Department of Health and Human Services). The quartic function
$$\begin{aligned}f(x)=&-0.056316 x^{4}-19.500154 x^{3} \\&+584.892054 x^{2}-1518.5717 x \\&+94,299.1990\end{aligned}$$
where $x$ is the number of years since $1990,$ can be used to estimate the number of twin births from 1990 to $2006 .$ Estimate the number of twin births in 1995 and in 2005
FIGURE CAN'T COPY

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 62

The greatest combined length of U.S.-owned operating railroad track existed in 1916, when industrial activity increased during World War I. The total length has decreased ever since. The data over the years 1900 to 2008 are modeled by the quartic function
$$\begin{aligned}f(x)=&-0.004091 x^{4}+1.275179 x^{3} \\&-142.589291 x^{2}+5069.1067 x \\&+197,909.1675\end{aligned}$$
where $x$ is the number of years since 1900 and $f(x)$ is in miles (Source: Association of American Railroads). Find the number of miles of operating railroad track in the United States in 1916 in $1960,$ and in $1985,$ and estimate the number in 2010 . (Note: The lengths exclude yard tracks, sidings, and parallel tracks.)

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 63

Dog Years. A dog's life span is typically much shorter than that of a human. The cubic function
$$\begin{aligned}d(x)=& 0.010255 x^{3}-0.340119 x^{2} \\&+7.397499 x+6.618361\end{aligned}$$
where $x$ is the dog's age, in years, approximates the equivalent human age in years. Estimate the equivalent human age for dogs that are $3,12,$ and 16 years old.

AG

Ankit Gupta

Numerade Educator

Problem 64

Threshold Weight. In a study performed by Alvin Shemesh, it was found that the threshold weight $W,$ defined as the weight above which the risk of death rises dramatically, is given by
$$W(h)=\left(\frac{h}{12.3}\right)^{3}$$
where $W$ is in pounds and $h$ is a person's height, in inches. Find the threshold weight of a person who is 5 ft 7 in. tall.

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Ankit Gupta

Numerade Educator

Problem 65

A stone thrown downward with an initial velocity of $34.3 \mathrm{m} / \mathrm{sec}$ will travel a distance of s meters, where
$$s(t)=4.9 t^{2}+34.3 t$$
and $t$ is in seconds. If a stone is thrown downward at $34.3 \mathrm{m} / \mathrm{sec}$ from a height of $294 \mathrm{m},$ how long will it take the stone to hit the ground?

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Ankit Gupta

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Problem 66

If there are $x$ teams in a sports league and all the teams play each other twice, a total of $N(x)$ games are played, where
$$N(x)=x^{2}-x$$
A softball league has 9 teams, each of which plays the others twice. If the league pays $\$ 110$ per game for the field and the umpires, how much will it cost to play the entire schedule?

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Ankit Gupta

Numerade Educator

Problem 67

The median price for an existing home in the United States peaked at $\$ 221,900$ in 2006 (Source: National Association of REALTORS $^{\infty}$ ). The quartic function
$$\begin{aligned}h(x)=& 56.8328 x^{4}-1554.7494 x^{3} \\&+10,451.8211 x^{2}-5655.7692 x \\&+140,589.1608\end{aligned}$$
where $x$ is the number of years since $2000,$ can be used to estimate the median existing-home price from 2000 to 2009 . Estimate the median existing-home price in $2002,$ in $2005,$ in 2008 and in 2009

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 68

In 1985 the circulation of daily newspapers reached its highest level (Source: Newspaper Association of America). The quartic function
$$\begin{aligned}f(x)=&-0.006093 x^{4}+0.849362 x^{3} \\&-51.892087 x^{2}+1627.3581 x \\&+41,334.7289\end{aligned}$$
where $x$ is the number of years since $1940,$ can be used to estimate the circulation of daily newspapers, in thousands, from 1940 to 2008 . Using this function, estimate the circulation of daily newspapers in $1945,$ in $1985,$ and in 2008

AG

Ankit Gupta

Numerade Educator

Problem 69

When $P$ dollars is invested at interest rate $i,$ compounded annually, for $t$ years, the investment grows to $A$ dollars, where
$$A=P(1+i)^{t}$$
Trevor's parents deposit $\$ 8000$ in a savings account when Trevor is 16 years old. The principal plus interest is to be used for a truck when Trevor is 18 years old. Find the interest rate $i$ if the $\$ 8000$ grows to $\$ 9039.75$ in 2 years.

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Ankit Gupta

Numerade Educator

Problem 70

When $P$ dollars is invested at interest rate $i,$ compounded annually, for $t$ years, the investment grows to $A$ dollars, where
$$A=P(1+i)^{t}$$
When Sara enters the 11 th grade, her grandparents deposit $\$ 10,000$ in a college savings account. Find the interest rate $i$ if the $\$ 10,000$ grows to $\$ 11,193.64$ in 2 years.

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Ankit Gupta

Numerade Educator

Problem 71

Determine which, if any, of the following functions might be used as a model for the data.
a) Linear, $f(x)=m x+b$
b) Quadratic, $f(x)=a x^{2}+b x+c, a>0$
c) Quadratic$, f(x)=a x^{2}+b x+c, a<0$
d) Polynomial, not linear or quadratic
(GRAPH CAN'T COPY)

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 72

Determine which, if any, of the following functions might be used as a model for the data.
a) Linear, $f(x)=m x+b$
b) Quadratic, $f(x)=a x^{2}+b x+c, a>0$
c) Quadratic$, f(x)=a x^{2}+b x+c, a<0$
d) Polynomial, not linear or quadratic
(GRAPH CAN'T COPY)

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 73

Determine which, if any, of the following functions might be used as a model for the data.
a) Linear, $f(x)=m x+b$
b) Quadratic, $f(x)=a x^{2}+b x+c, a>0$
c) Quadratic$, f(x)=a x^{2}+b x+c, a<0$
d) Polynomial, not linear or quadratic
(GRAPH CAN'T COPY)

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 74

Determine which, if any, of the following functions might be used as a model for the data.
a) Linear, $f(x)=m x+b$
b) Quadratic, $f(x)=a x^{2}+b x+c, a>0$
c) Quadratic$, f(x)=a x^{2}+b x+c, a<0$
d) Polynomial, not linear or quadratic
(GRAPH CAN'T COPY)

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 75

Determine which, if any, of the following functions might be used as a model for the data.
a) Linear, $f(x)=m x+b$
b) Quadratic, $f(x)=a x^{2}+b x+c, a>0$
c) Quadratic$, f(x)=a x^{2}+b x+c, a<0$
d) Polynomial, not linear or quadratic
(GRAPH CAN'T COPY)

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 76

Determine which, if any, of the following functions might be used as a model for the data.
a) Linear, $f(x)=m x+b$
b) Quadratic, $f(x)=a x^{2}+b x+c, a>0$
c) Quadratic$, f(x)=a x^{2}+b x+c, a<0$
d) Polynomial, not linear or quadratic
(GRAPH CAN'T COPY)

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 77

Foreign Adoptions. The number of foreign adoptions in the United States has declined in recent years, as shown in the table below.
(TABLE CAN'T COPY)
a) Use a graphing calculator to fit quadratic, cubic, and quartic functions to the data. Let $x$ represent the number of years since $2000 .$ Using $R^{2}$ -values, determine which function is the best fit.
b) Using the function found in part (a), estimate the number of U.S. foreign adoptions in 2010.

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 78

U.S. Farm Acreage. As the number of farms has decreased in the United States, the average size of the remaining farms has grown larger, as shown in the table below.
(TABLE CAN'T COPY)
a) Use a graphing calculator to fit quadratic, cubic, and quartic functions to the data. Let $x$ represent the number of years since 1900 . Using $R^{2}$ -values, determine which function is the best fit.
b) Using the function found in part (a), estimate the average acreage in $1955,$ in $1998,$ and in 2011

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 79

Classified Ad Revenue. The table below lists the newspaper revenue from classified ads for selected years from 1975 to 2009.
TABLE CAN'T COPY
a) Use a graphing calculator to fit cubic and quartic functions to the data. Let $x$ represent the number of years since $1975 .$ Using $R^{2}$ -values, determine which function is the best fit.
b) Using the function found in part (a), estimate the newspaper revenue from classified ads in $1988,$ in $2002,$ and in 2010

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 80

A dog's life span is typically much shorter than that of a human. Age equivalents for dogs and humans are listed in the table below.
TABLE CAN'T COPY
a) Use a graphing calculator to fit linear and cubic functions to the data. Which function has the better fit?
b) Using the function from part (a), estimate the equivalent human age for dogs that are 5 ,
$10,$ and 15 years old.

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 81

Find the distance between the pair of points.
$$(3,-5)$ and $(0,-1)$$

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Ankit Gupta

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Problem 82

Find the distance between the pair of points.

$$(4,2)$ and $(-2,-4)$$

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Ankit Gupta

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Problem 83

Find the distance between the pair of points.

Find the center and the radius of the circle $(x-3)^{2}+(y+5)^{2}=49$

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 84

Find the distance between the pair of points.
The diameter of a circle connects the points $(-6,5)$ and $(-2,1)$ on the circle. Find the coordinates of the center of the circle and the length of the radius.

Darshan Maheshwari

Darshan Maheshwari

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Problem 85

Solve.
$$2 y-3 \geq 1-y+5$$

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Ankit Gupta

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Problem 86

Solve.

$$(x-2)(x+5)>x(x-3)$$

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Ankit Gupta

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Problem 87

Solve.

$$|x+6| \geq 7$$

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Ankit Gupta

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Problem 88

Solve.

$$\left|x+\frac{1}{4}\right| \leq \frac{2}{3}$$

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Ankit Gupta

Numerade Educator

Problem 89

Determine the degree and the leading term of the polynomial function.
$$f(x)=\left(x^{5}-1\right)^{2}\left(x^{2}+2\right)^{3}$$

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Ankit Gupta

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Problem 90

Determine the degree and the leading term of the polynomial function.

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

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Ankit Gupta

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