Question 1

Find the zeros of the function.
-$$f ( x ) = x ^ { 3 } - 49 x$$

Accepted Answer

A)  0 and 7 
B)  1,7 , and $- 7$ 
C)  7 and $- 7$ 
D)  0,7 , and $- 7$ 
A)  0 and 7 
B)  1,7 , and $- 7$ 
C)  7 and $- 7$ 
D)  0,7 , and $- 7$

Question 2

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative.
-$$f ( x ) = \frac { ( x - 2 ) } { ( 2 x + 1 ) ( x - 3 ) }$$

Accepted Answer

A)  (a) $ \left\{2,3,-\frac{1}{2}\right\} $ (b) $ \varnothing $, (c) $ \left(-\infty,-\frac{1}{2}\right) \cup(2,3) $, (d) $ \left(-\frac{1}{2}, 2\right) \cup(3, \infty) $ 
B)  (a) $ \{3\} $, (b) $ \left\{3,-\frac{1}{2}\right\} $, (c) $ \left(-\infty,-\frac{1}{2}\right) \cup(2,3),(\mathrm{d})\left(-\frac{1}{2}, 2\right) \cup(3, \infty) $ 
C)  (a) $ \{2,3\} $, (b) $ \left\{-\frac{1}{2}\right\} $ (c) $ \left\{-\frac{1}{2}, 2\right) \cup(3, \infty),(\mathrm{d})\left(-\infty,-\frac{1}{2}\right) \cup(2,3) $ 
D)  (a) $ \{2\} $, (b) $ \left\{3,-\frac{1}{2}\right\} $, (c) $ \left\{-\frac{1}{2}, 2\right) \cup(3, \infty),(d)\left(-\infty,-\frac{1}{2}\right) \cup(2,3) $ 
A)  (a) $ \left\{2,3,-\frac{1}{2}\right\} $ (b) $ \varnothing $, (c) $ \left(-\infty,-\frac{1}{2}\right) \cup(2,3) $, (d) $ \left(-\frac{1}{2}, 2\right) \cup(3, \infty) $ 
B)  (a) $ \{3\} $, (b) $ \left\{3,-\frac{1}{2}\right\} $, (c) $ \left(-\infty,-\frac{1}{2}\right) \cup(2,3),(\mathrm{d})\left(-\frac{1}{2}, 2\right) \cup(3, \infty) $ 
C)  (a) $ \{2,3\} $, (b) $ \left\{-\frac{1}{2}\right\} $ (c) $ \left\{-\frac{1}{2}, 2\right) \cup(3, \infty),(\mathrm{d})\left(-\infty,-\frac{1}{2}\right) \cup(2,3) $ 
D)  (a) $ \{2\} $, (b) $ \left\{3,-\frac{1}{2}\right\} $, (c) $ \left\{-\frac{1}{2}, 2\right) \cup(3, \infty),(d)\left(-\infty,-\frac{1}{2}\right) \cup(2,3) $

Question 3

Write a linear factorization of the function.
-$$f ( x ) = x ^ { 4 } + 61 x ^ { 2 } + 900$$

Accepted Answer

A)  $f ( x ) = ( x + 30 i ) ^ { 4 }$ 
B)  $f ( x ) = ( x + i ) ( x - i ) ( x + 30 i ) ( x - 30 i )$ 
C)  $f ( x ) = \left( x ^ { 2 } + 30 i \right) \left( x ^ { 2 } - 30 i \right)$ 
D)  $f ( x ) = ( x + 5 i ) ( x - 5 i ) ( x + 6 i ) ( x - 6 i )$ 
A)  $f ( x ) = ( x + 30 i ) ^ { 4 }$ 
B)  $f ( x ) = ( x + i ) ( x - i ) ( x + 30 i ) ( x - 30 i )$ 
C)  $f ( x ) = \left( x ^ { 2 } + 30 i \right) \left( x ^ { 2 } - 30 i \right)$ 
D)  $f ( x ) = ( x + 5 i ) ( x - 5 i ) ( x + 6 i ) ( x - 6 i )$

Question 4

Solve the problem.
-The table shows the population of a certain city in various years. The population of the city $f ( x )$, in hundreds of thousands, can be modeled by $f ( x ) = a x ^ { b }$, where $x$ represents the number of years since 1980 . Estimate the population of the city in the year 1986. (You will first need to use regression to estimate the values of a and b).

Accepted Answer

A)  617,869 
B)  656,499 
C)  586,160 
D)  679,946 
A)  617,869 
B)  656,499 
C)  586,160 
D)  679,946

Question 5

Use limits to describe the behavior of the rational function near the indicated asymptote.
-$$f ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }$$
Describe the behavior of the function near its horizontal asymptote (the end behavior).

Accepted Answer

A)  $\lim _ { x \rightarrow \infty } f ( x ) = - \infty , \quad \lim _ { x \rightarrow } f ( x ) = \infty$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = - 1 , \lim _ { x \rightarrow \infty } f ( x ) = 1$ 
C)  $\lim _ { x \rightarrow \infty } f ( x ) = 0 , \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
D)  $\lim _ { x - \theta ^ { - } } f ( x ) = \infty , \quad \lim _ { x - \theta ^ { + } } f ( x ) = \infty$ 
A)  $\lim _ { x \rightarrow \infty } f ( x ) = - \infty , \quad \lim _ { x \rightarrow } f ( x ) = \infty$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = - 1 , \lim _ { x \rightarrow \infty } f ( x ) = 1$ 
C)  $\lim _ { x \rightarrow \infty } f ( x ) = 0 , \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
D)  $\lim _ { x - \theta ^ { - } } f ( x ) = \infty , \quad \lim _ { x - \theta ^ { + } } f ( x ) = \infty$

Question 6

Using the given zero, find all other zeros of f(x).
-$3 i$ is a zero of $f ( x ) = 16 x ^ { 4 } - 8 x ^ { 3 } + 154 x ^ { 2 } - 72 x + 90$

Accepted Answer

A)  $- 3 \mathrm { i } , \frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i } , \frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }$ 
B)  $- 3 \mathrm { i } , - \frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i } , - \frac { 1 } { 4 } - \frac { \sqrt { 3 } } { 4 } \mathrm { i }$ 
C)  $- 3 \mathrm { i } , \frac { 1 } { 4 } + \frac { 3 } { 4 } \mathrm { i } , \frac { 1 } { 4 } - \frac { 3 } { 4 } \mathrm { i }$ 
D)  $- 3 \mathrm { i } , - \frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i } , - \frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }$ 
A)  $- 3 \mathrm { i } , \frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i } , \frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }$ 
B)  $- 3 \mathrm { i } , - \frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i } , - \frac { 1 } { 4 } - \frac { \sqrt { 3 } } { 4 } \mathrm { i }$ 
C)  $- 3 \mathrm { i } , \frac { 1 } { 4 } + \frac { 3 } { 4 } \mathrm { i } , \frac { 1 } { 4 } - \frac { 3 } { 4 } \mathrm { i }$ 
D)  $- 3 \mathrm { i } , - \frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i } , - \frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }$

Question 7

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the
polynomial in standard form.
-2 (multiplicity 1 ) and $- 4$ (multiplicity 3 )

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 24 x ^ { 2 } - 32 x - 128$ 
B)  $f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 24 x ^ { 2 } + 32 x - 128$ 
C)  $f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 24 x ^ { 2 } - 32 x - 128$ 
D)  $f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 24 x ^ { 2 } - 32 x + 128$ 
A)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 24 x ^ { 2 } - 32 x - 128$ 
B)  $f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 24 x ^ { 2 } + 32 x - 128$ 
C)  $f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 24 x ^ { 2 } - 32 x - 128$ 
D)  $f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 24 x ^ { 2 } - 32 x + 128$

Question 8

Solve the problem.
-A rectangular enclosure must have an area of at least $5400 \mathrm { yd } 2$. If $300 \mathrm { yd }$ of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Accepted Answer

A)  $60 \leq w \leq 90$ 
B)  $60 \leq w \leq 75$ 
C)  $0 \leq w \leq 60$ 
D)  $75 \leq w \leq 90$ 
A)  $60 \leq w \leq 90$ 
B)  $60 \leq w \leq 75$ 
C)  $0 \leq w \leq 60$ 
D)  $75 \leq w \leq 90$

Question 9

Provide an appropriate response.
-Is it possible to have a polynomial function whose only zeros are 2 and i? If so, write such a function. If not, explain why.

Accepted Answer

A)  No; the Complex Conjugate Zeros Statement requires that - i must also be a zero. 
B)  Yes; $f ( x ) = x ^ { 2 } - ( 2 - i ) x - 2 i$ is such a function. 
C)  No; the Complex Conjugate Zeros Statement requires that $- 2$ and $- \mathrm { i }$ must also be zeros. 
D)  Yes; $f ( x ) = x ^ { 2 } - ( 2 + i ) x + 2 i$ is such a function. 
A)  No; the Complex Conjugate Zeros Statement requires that - i must also be a zero. 
B)  Yes; $f ( x ) = x ^ { 2 } - ( 2 - i ) x - 2 i$ is such a function. 
C)  No; the Complex Conjugate Zeros Statement requires that $- 2$ and $- \mathrm { i }$ must also be zeros. 
D)  Yes; $f ( x ) = x ^ { 2 } - ( 2 + i ) x + 2 i$ is such a function.

Question 10

Solve the problem.
-The ages and lengths of several animals of the same species are recorded in the following table:

Use linear regression to predict the length of a 35 -month-old animal.

Accepted Answer

A)  $37.50$ in 
B)  $35.60$ in 
C)  $38.50$ in 
D)  $36.60$ in 
A)  $37.50$ in 
B)  $35.60$ in 
C)  $38.50$ in 
D)  $36.60$ in

Question 11

Solve the polynomial inequality.
-$$( x + 8 ) \left( x ^ { 2 } - 25 \right) > 0$$

Accepted Answer

A)  $( - 8 , - 5 ) \cup ( 5 , \infty )$ 
B)  $( - \infty , - 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , 5 ) \cup ( 5,8 )$ 
D)  $( - 8,5 )$ 
A)  $( - 8 , - 5 ) \cup ( 5 , \infty )$ 
B)  $( - \infty , - 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , 5 ) \cup ( 5,8 )$ 
D)  $( - 8,5 )$

Question 12

Provide an appropriate response.
-Consider the graph of the polynomial function $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 3 x - 9$. What are the linear factors of $P ( x )$ ?

Accepted Answer

A)  $x + 3 , x - 1 , x + 6$ 
B)  $x + 1 , x + 3 , x + 5$ 
C)  $x + 3 , x - 1 , x + 3$ 
D)  $x - 3 , x - 1 , x - 3$ 
A)  $x + 3 , x - 1 , x + 6$ 
B)  $x + 1 , x + 3 , x + 5$ 
C)  $x + 3 , x - 1 , x + 3$ 
D)  $x - 3 , x - 1 , x - 3$

Question 13

Find all rational zeros.
-$$f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 14 x + 24$$

Accepted Answer

A)  $- 5 , - 7,1$ 
B)  $5,7 , - 1$ 
C)  $- 4 , - 6,1$ 
D)  $4,6 , - 1$ 
A)  $- 5 , - 7,1$ 
B)  $5,7 , - 1$ 
C)  $- 4 , - 6,1$ 
D)  $4,6 , - 1$

Question 14

Determine whether the power function is even, odd, or neither.
-$$f ( x ) = - x ^ { - 8 }$$

Accepted Answer

A)  Even 
B)  Neither 
C)  Odd 
A)  Even 
B)  Neither 
C)  Odd

Find the zeros of the function. - $f ( x ) = x ^ { 3 } - 49 x$

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { ( x - 2 ) } { ( 2 x + 1 ) ( x - 3 ) }$

Write a linear factorization of the function. - $f ( x ) = x ^ { 4 } + 61 x ^ { 2 } + 900$

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }$ Describe the behavior of the function near its horizontal asymptote (the end behavior).

Using the given zero, find all other zeros of f(x). - $3 i$ is a zero of $f ( x ) = 16 x ^ { 4 } - 8 x ^ { 3 } + 154 x ^ { 2 } - 72 x + 90$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -2 (multiplicity 1 ) and $- 4$ (multiplicity 3 )

Solve the problem. -A rectangular enclosure must have an area of at least $5400 \mathrm { yd } 2$ . If $300 \mathrm { yd }$ of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Provide an appropriate response. -Is it possible to have a polynomial function whose only zeros are 2 and i? If so, write such a function. If not, explain why.

Solve the problem. -The ages and lengths of several animals of the same species are recorded in the following table: Use linear regression to predict the length of a 35 -month-old animal.

Solve the polynomial inequality. - $( x + 8 ) \left( x ^ { 2 } - 25 \right) > 0$

Find all rational zeros. - $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 14 x + 24$

Determine whether the power function is even, odd, or neither. - $f ( x ) = - x ^ { - 8 }$

Functions and Graphs

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 2: Polynomial, Power, and Rational Functions

Find the zeros of the function. - f(x)=x3−49xf ( x ) = x ^ { 3 } - 49 xf(x)=x3−49x

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - f(x)=(x−2)(2x+1)(x−3)f ( x ) = \frac { ( x - 2 ) } { ( 2 x + 1 ) ( x - 3 ) }f(x)=(2x+1)(x−3)(x−2)​

Write a linear factorization of the function. - f(x)=x4+61x2+900f ( x ) = x ^ { 4 } + 61 x ^ { 2 } + 900f(x)=x4+61x2+900

Use limits to describe the behavior of the rational function near the indicated asymptote. - f(x)=x+1x2−2xf ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }f(x)=x2−2xx+1​ Describe the behavior of the function near its horizontal asymptote (the end behavior).

Using the given zero, find all other zeros of f(x). - 3i3 i3i is a zero of f(x)=16x4−8x3+154x2−72x+90f ( x ) = 16 x ^ { 4 } - 8 x ^ { 3 } + 154 x ^ { 2 } - 72 x + 90f(x)=16x4−8x3+154x2−72x+90

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -2 (multiplicity 1 ) and −4- 4−4 (multiplicity 3 )

Solve the problem. -A rectangular enclosure must have an area of at least 5400yd25400 \mathrm { yd } 25400yd2 . If 300yd300 \mathrm { yd }300yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?