Question 1

Determine whether the power function is even, odd, or neither.
-$$f ( x ) = 7 x ^ { 1 / 8 }$$

Accepted Answer

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

Question 2

Solve the problem.
-The function $N ( t ) = \frac { 0.5 t + 1000 } { 6 t + 5 } , t \geq 8$
gives the body concentration $\mathrm { N } ( \mathrm { t } )$, in parts per million, of a certain dosage of medication after time $t$, in hours.
Graph the function on the interval $[ 8 , \infty )$ and complete the following:
$\mathrm { N } ( \mathrm { t } ) \rightarrow \quad$ as $\mathrm { t } \rightarrow \mathrm { x } _ { \text {. } }$

Accepted Answer

A) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 0$ as $\mathrm { t } \rightarrow \infty
 $ 
B) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 0.083$ as $\mathrm { t } \rightarrow \infty .$ 
C) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 1$ as $\mathrm { t } \rightarrow\infty  $ 
D) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 0.071$ as $\mathrm { t } \rightarrow \infty$, 
A) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 0$ as $\mathrm { t } \rightarrow \infty
 $ 
B) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 0.083$ as $\mathrm { t } \rightarrow \infty .$ 
C) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 1$ as $\mathrm { t } \rightarrow\infty  $ 
D) 
 
$\mathrm { N } ( \mathrm { t } ) \rightarrow 0.071$ as $\mathrm { t } \rightarrow \infty$,

Question 3

For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { x + 9 } { x ^ { 2 } + 9 x + 2 }$, horizontal

Accepted Answer

A)  $y = 0$ 
B)  None 
C)  $y = x$ 
D)  $y = 9$ 
A)  $y = 0$ 
B)  None 
C)  $y = x$ 
D)  $y = 9$

Question 4

Provide an appropriate response.
-Suppose that a polynomial function $f$ is defined in such a way that $f ( - 4.7 ) = - 3$ and $f ( 5 ) = 1$. What conclusion does the Intermediate Value Theorem allow you to make?

Accepted Answer

A)  There must be a zero between $- 3$ and 1 . 
B)  There must be two zeros between $- 4.7$ and 5 . 
C)  There must be a zero between $- 4.7$ and 5 . 
D)  There is not enough information to draw a conclusion about the zeros of $f$. 
A)  There must be a zero between $- 3$ and 1 . 
B)  There must be two zeros between $- 4.7$ and 5 . 
C)  There must be a zero between $- 4.7$ and 5 . 
D)  There is not enough information to draw a conclusion about the zeros of $f$.

Question 5

Divide f(x) by d(x), and write a summary statement in the form indicated.
-$f ( x ) = x ^ { 2 } - 2 x + 3 ; d ( x ) = x - 6 \quad$ (Write answer in polynomial form)

Accepted Answer

A)  $f ( x ) = ( x - 6 ) ^ { 2 } + 24$ 
B)  $f ( x ) = ( x - 6 ) ( x + 4 ) + 27$ 
C)  $f ( x ) = ( x - 6 ) ^ { 2 } + 27$ 
D)  $f ( x ) = ( x - 6 ) ( x + 4 ) + 24$ 
A)  $f ( x ) = ( x - 6 ) ^ { 2 } + 24$ 
B)  $f ( x ) = ( x - 6 ) ( x + 4 ) + 27$ 
C)  $f ( x ) = ( x - 6 ) ^ { 2 } + 27$ 
D)  $f ( x ) = ( x - 6 ) ( x + 4 ) + 24$

Question 6

Using the given zero, find all other zeros of f(x).
-$- 2 i$ is a zero of $f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144$

Accepted Answer

A)  $2 i , 12 , - 12$ 
B)  $2 \mathrm { i } , 6 , - 6$ 
C)  $2 \mathrm { i } , 6 \mathrm { i } , - 6 \mathrm { i }$ 
D)  $2 \mathrm { i } , 12 \mathrm { i } , - 12 \mathrm { i }$ 
A)  $2 i , 12 , - 12$ 
B)  $2 \mathrm { i } , 6 , - 6$ 
C)  $2 \mathrm { i } , 6 \mathrm { i } , - 6 \mathrm { i }$ 
D)  $2 \mathrm { i } , 12 \mathrm { i } , - 12 \mathrm { i }$

Question 7

Data are given for y as a power function of x. Write an equation for the power function, and state its power and constant
of variation.
-

Accepted Answer

A)  $\mathrm { y } = 2 \sqrt [ 3 ] { \mathrm { x } } ;$ Power $= \frac { 1 } { 3 } ;$ constant of variation $= 2$ 
B)  $\mathrm { y } = 0.5 \mathrm { x }$; Power $= 1$; constant of variation $= 0.5$ 
C)  $\mathrm { y } = 2 \sqrt [ 3 ] { \mathrm { x } }$; Power $= - 3$; constant of variation $= 2$ 
D)  $\mathrm { y } = \sqrt { \mathrm { x } }$; Power $= \frac { 1 } { 2 }$; constant of variation $= 1$ 
A)  $\mathrm { y } = 2 \sqrt [ 3 ] { \mathrm { x } } ;$ Power $= \frac { 1 } { 3 } ;$ constant of variation $= 2$ 
B)  $\mathrm { y } = 0.5 \mathrm { x }$; Power $= 1$; constant of variation $= 0.5$ 
C)  $\mathrm { y } = 2 \sqrt [ 3 ] { \mathrm { x } }$; Power $= - 3$; constant of variation $= 2$ 
D)  $\mathrm { y } = \sqrt { \mathrm { x } }$; Power $= \frac { 1 } { 2 }$; constant of variation $= 1$

Question 8

Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( - 3 , - 4 )$, point $( - 6,5 )$

Accepted Answer

A)  $P ( x ) = - x ^ { 2 } + 6 x + 4$ 
B)  $P ( x ) = - 6 x ^ { 2 } - 6 x - 5$ 
C)  $\mathrm { P } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 4$ 
D)  $P ( x ) = x ^ { 2 } + 6 x + 5$ 
A)  $P ( x ) = - x ^ { 2 } + 6 x + 4$ 
B)  $P ( x ) = - 6 x ^ { 2 } - 6 x - 5$ 
C)  $\mathrm { P } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 4$ 
D)  $P ( x ) = x ^ { 2 } + 6 x + 5$

Question 9

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest
hundredth.
-

Accepted Answer

A)  $y \approx 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.30 x + 15.00$ 
B)  $y = - 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.30 x + 15.00$ 
C)  $y = - 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.10 x + 15.00$ 
D)  $y \approx 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.10 x + 15.00$ 
A)  $y \approx 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.30 x + 15.00$ 
B)  $y = - 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.30 x + 15.00$ 
C)  $y = - 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.10 x + 15.00$ 
D)  $y \approx 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.10 x + 15.00$

Question 10

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of
the function f.
-$k = 3 ; f ( x ) = 3 x ^ { 4 } + 2 x ^ { 3 } - 2 x ^ { 2 } + 5 x + 1$; Upper bound?

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 11

Solve the problem.
-A $53 \mathrm {~m}$-long steel beam is anchored at one end to a piling $7 \mathrm {~m}$ above the ground. Assume that when a certain heavy object is placed $\mathrm { d }$ meters from the anchored end, the beam bends s meters where
$$s = \left( 3 \times 10 ^ { - 6 } \right) d ^ { 2 } ( 150 - d ) \text {. }$$
How far is the heavy object from the anchored end if the vertical deflection is $0.50 \mathrm {~m}$ ? (Round to the nearest hundred)

Accepted Answer

A)  $141.70 \mathrm {~m}$ 
B)  $38.70 \mathrm {~m}$ 
C)  $30.40 \mathrm {~m}$ 
D)  $27.50 \mathrm {~m}$ 
A)  $141.70 \mathrm {~m}$ 
B)  $38.70 \mathrm {~m}$ 
C)  $30.40 \mathrm {~m}$ 
D)  $27.50 \mathrm {~m}$

Question 12

State how many complex and real zeros the function has.
-$$f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 5 x - 2$$

Accepted Answer

A)  3 complex zeros; 2 real 
B)  3 complex zeros; 1 real 
C)  3 complex zeros; none real 
D)  3 complex zeros; all 3 real 
A)  3 complex zeros; 2 real 
B)  3 complex zeros; 1 real 
C)  3 complex zeros; none real 
D)  3 complex zeros; all 3 real

Question 13

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros: $3 , \mathrm { i } , - \mathrm { i } ; \mathrm { f } ( 2 ) = 15$

Accepted Answer

A)  $- 3 x ^ { 3 } + 9 x ^ { 2 } - 3 x + 9$ 
B)  $3 x ^ { 3 } - 9 x ^ { 2 } - 3 x + 9$ 
C)  $- 3 x ^ { 3 } + 9 x ^ { 2 } + 3 x - 9$ 
D)  $3 x ^ { 3 } - 9 x ^ { 2 } + 3 x - 9$ 
A)  $- 3 x ^ { 3 } + 9 x ^ { 2 } - 3 x + 9$ 
B)  $3 x ^ { 3 } - 9 x ^ { 2 } - 3 x + 9$ 
C)  $- 3 x ^ { 3 } + 9 x ^ { 2 } + 3 x - 9$ 
D)  $3 x ^ { 3 } - 9 x ^ { 2 } + 3 x - 9$

Question 14

Find all rational zeros.
-$$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32$$

Accepted Answer

A)  $- 2 , - 4,4$ 
B)  $3,4 , - 8$ 
C)  $2,4 , - 4$ 
D)  $- 3 , - 4,8$ 
A)  $- 2 , - 4,4$ 
B)  $3,4 , - 8$ 
C)  $2,4 , - 4$ 
D)  $- 3 , - 4,8$

Question 15

For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { x ^ { 2 } + 4 x - 4 } { x - 4 }$, horizontal

Accepted Answer

A)  $y = 4$ 
B)  $y = - 4$ 
C)  None 
D)  $y = 3$ 
A)  $y = 4$ 
B)  $y = - 4$ 
C)  None 
D)  $y = 3$

Question 16

Write the quadratic function in vertex form.
-$$y = x ^ { 2 } - 20 x$$

Accepted Answer

A)  $y = ( x + 10 ) ^ { 2 } - 10$ 
B)  $y = ( x + 20 ) ^ { 2 } - 20$ 
C)  $y = ( x - 10 ) ^ { 2 } - 100$ 
D)  $y = ( x - 20 ) ^ { 2 } - 400$ 
A)  $y = ( x + 10 ) ^ { 2 } - 10$ 
B)  $y = ( x + 20 ) ^ { 2 } - 20$ 
C)  $y = ( x - 10 ) ^ { 2 } - 100$ 
D)  $y = ( x - 20 ) ^ { 2 } - 400$

Question 17

Write the word or phrase that best completes each statement or answers the question.
Write a sentence that expresses the relationship in the formula, using the language of variation or proportion.
-$$\mathrm { f } - \text { stop } = \frac { \mathrm { f } } { \mathrm { D } } \text {, where } \mathrm { f } - \text { stop is camera setting with a lens with focal length } \mathrm { f } \text { and diaphragm opening } \mathrm { D }$$

Accepted Answer

A camera's f-stop va

Question 18

State how many complex and real zeros the function has.
-$$f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 5 x ^ { 2 } - 4 x + 4$$

Accepted Answer

A)  4 complex zeros; none real 
B)  4 complex zeros; all 4 real 
C)  4 complex zeros; 2 real 
D)  4 complex zeros; 1 real 
A)  4 complex zeros; none real 
B)  4 complex zeros; all 4 real 
C)  4 complex zeros; 2 real 
D)  4 complex zeros; 1 real

Question 19

Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( 4,1 )$, point $( - 1,76 )$

Accepted Answer

A)  $P ( x ) = - 24 x + 49$ 
B)  $P ( x ) = 3 x ^ { 2 } - 24 x + 49$ 
C)  $P ( x ) = 3 x ^ { 2 } - 4 x + 1$ 
D)  $P ( x ) = - 3 x ^ { 2 } - 24 x + 1$ 
A)  $P ( x ) = - 24 x + 49$ 
B)  $P ( x ) = 3 x ^ { 2 } - 24 x + 49$ 
C)  $P ( x ) = 3 x ^ { 2 } - 4 x + 1$ 
D)  $P ( x ) = - 3 x ^ { 2 } - 24 x + 1$

Question 20

Solve the problem.
-Find the remainder when $x ^ { 44 } - 19$ is divided by $x + 1$.

Accepted Answer

A)  18 
B)  $- 20$ 
C)  $- 18$ 
D)  20 
A)  18 
B)  $- 20$ 
C)  $- 18$ 
D)  20

Determine whether the power function is even, odd, or neither. - $f ( x ) = 7 x ^ { 1 / 8 }$

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { x + 9 } { x ^ { 2 } + 9 x + 2 }$ , horizontal

Provide an appropriate response. -Suppose that a polynomial function $f$ is defined in such a way that $f ( - 4.7 ) = - 3$ and $f ( 5 ) = 1$ . What conclusion does the Intermediate Value Theorem allow you to make?

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 2 } - 2 x + 3 ; d ( x ) = x - 6 \quad$ (Write answer in polynomial form)

Using the given zero, find all other zeros of f(x). - $- 2 i$ is a zero of $f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144$

Data are given for y as a power function of x. Write an equation for the power function, and state its power and constant of variation. -

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( - 3 , - 4 )$ , point $( - 6,5 )$

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. - $k = 3 ; f ( x ) = 3 x ^ { 4 } + 2 x ^ { 3 } - 2 x ^ { 2 } + 5 x + 1$ ; Upper bound?

State how many complex and real zeros the function has. - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 5 x - 2$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros: $3 , \mathrm { i } , - \mathrm { i } ; \mathrm { f } ( 2 ) = 15$

Find all rational zeros. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32$

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { x ^ { 2 } + 4 x - 4 } { x - 4 }$ , horizontal

Write the quadratic function in vertex form. - $y = x ^ { 2 } - 20 x$

State how many complex and real zeros the function has. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 5 x ^ { 2 } - 4 x + 4$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( 4,1 )$ , point $( - 1,76 )$

Solve the problem. -Find the remainder when $x ^ { 44 } - 19$ is divided by $x + 1$ .

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

Determine whether the power function is even, odd, or neither. - f(x)=7x1/8f ( x ) = 7 x ^ { 1 / 8 }f(x)=7x1/8

For the given function, find all asymptotes of the type indicated (if there are any) - f(x)=x+9x2+9x+2f ( x ) = \frac { x + 9 } { x ^ { 2 } + 9 x + 2 }f(x)=x2+9x+2x+9​ , horizontal

Provide an appropriate response. -Suppose that a polynomial function fff is defined in such a way that f(−4.7)=−3f ( - 4.7 ) = - 3f(−4.7)=−3 and f(5)=1f ( 5 ) = 1f(5)=1 . What conclusion does the Intermediate Value Theorem allow you to make?

Divide f(x) by d(x), and write a summary statement in the form indicated. - f(x)=x2−2x+3;d(x)=x−6f ( x ) = x ^ { 2 } - 2 x + 3 ; d ( x ) = x - 6 \quadf(x)=x2−2x+3;d(x)=x−6 (Write answer in polynomial form)

Using the given zero, find all other zeros of f(x). - −2i- 2 i−2i is a zero of f(x)=x4−32x2−144f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144f(x)=x4−32x2−144