Question 1

Find the vertex of the graph of the function.
-$f ( x ) = 4 x ^ { 2 } + 16 x + 21$

Accepted Answer

A)  $( - 4,3 )$ 
B)  $( 5 , - 2 )$ 
C)  $( 3 , - 4 )$ 
D)  $( - 2,5 )$ 
A)  $( - 4,3 )$ 
B)  $( 5 , - 2 )$ 
C)  $( 3 , - 4 )$ 
D)  $( - 2,5 )$

Question 2

Write an equation for the linear function f satisfying the given conditions.
-$f ( - 3 ) = 8$ and $f ( 1 ) = 4$

Accepted Answer

A)  $f ( x ) = - 3 x - 1$ 
B)  $f ( x ) = - x + 5$ 
C)  $f ( x ) = 3 x + 1$ 
D)  $f ( x ) = - \frac { 8 } { 3 } x$ 
A)  $f ( x ) = - 3 x - 1$ 
B)  $f ( x ) = - x + 5$ 
C)  $f ( x ) = 3 x + 1$ 
D)  $f ( x ) = - \frac { 8 } { 3 } x$

Question 3

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative.
-$$f ( x ) = \left( 2 x ^ { 2 } + 3 \right) ( x - 6 ) ^ { 2 } ( x + 9 ) ^ { 3 }$$

Accepted Answer

A)  (a) $\{ - 9,6 \}$, (b) $( - 9 , \infty )$, (c) $( \infty , - 9 )$ 
B)  (a) $\{ - 9,6 \}$, (b) $( - 9,6 )$ (c) $( - 9 , \infty ) \cup ( 6 , \infty )$ 
C)  (a) $\{ - 9,6 \}$, (b) $( - 9,6 ) \cup ( 6 , \infty ) ($ c) $( x , - 9 )$ 
D)  (a) $\{ - 9,6 \}$, (b) $( 6 , \infty )$, (c) $( \infty , 6 )$ 
A)  (a) $\{ - 9,6 \}$, (b) $( - 9 , \infty )$, (c) $( \infty , - 9 )$ 
B)  (a) $\{ - 9,6 \}$, (b) $( - 9,6 )$ (c) $( - 9 , \infty ) \cup ( 6 , \infty )$ 
C)  (a) $\{ - 9,6 \}$, (b) $( - 9,6 ) \cup ( 6 , \infty ) ($ c) $( x , - 9 )$ 
D)  (a) $\{ - 9,6 \}$, (b) $( 6 , \infty )$, (c) $( \infty , 6 )$

Question 4

Describe how to transform the graph of an appropriate monomial function f(x) = xn into the graph of the given
polynomial function. Then sketch the transformed graph.
-$$g ( x ) = - ( x + 2 ) ^ { 3 }$$

Accepted Answer

Obtain the graph of @#LAT-DLM& by shifti

Question 5

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros: $- 3 , - 1,4 ; f ( 2 ) = 10$

Accepted Answer

A)  $\frac { - x ^ { 3 } } { 3 } + \frac { 13 x } { 3 } + 4$ 
B)  $\frac { - x ^ { 3 } } { 3 } - \frac { 19 x } { 3 } - 4$ 
C)  $\frac { x ^ { 3 } } { 3 } - \frac { 13 x } { 3 } - 4$ 
D)  $\frac { x ^ { 3 } } { 3 } + \frac { 19 x } { 3 } - 4$ 
A)  $\frac { - x ^ { 3 } } { 3 } + \frac { 13 x } { 3 } + 4$ 
B)  $\frac { - x ^ { 3 } } { 3 } - \frac { 19 x } { 3 } - 4$ 
C)  $\frac { x ^ { 3 } } { 3 } - \frac { 13 x } { 3 } - 4$ 
D)  $\frac { x ^ { 3 } } { 3 } + \frac { 19 x } { 3 } - 4$

Question 6

Solve the problem. Round as appropriate.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2.5 sec when the length is 25 inches, what is the period when L = 3.0625 inches?

Accepted Answer

A)  3.5 sec 
B)  3.25 sec 
C)  3 sec 
D)  0.875 sec 
A)  3.5 sec 
B)  3.25 sec 
C)  3 sec 
D)  0.875 sec

Question 7

Provide an appropriate response.
-Suppose that $\mathrm { f }$ is a polynomial function of degree 4 . If $- 5$ and 11 are zeros of $f$ and the graph of $f$ is symmetric with respect to the $y$-axis, write $f ( x )$ in factored form.

Accepted Answer

A)  $f ( x ) = ( x + 5 ) ^ { 2 } ( x - 11 ) ^ { 2 }$ 
B)  $f ( x ) = ( x + 5 ) ( x - 11 ) ( x - 5 ) ( x + 11 )$ 
C)  $f ( x ) = ( x + 5 ) ( x - 11 )$ 
D)  $f ( x ) = ( x - 5 ) ^ { 2 } ( x + 11 ) ^ { 2 }$ 
A)  $f ( x ) = ( x + 5 ) ^ { 2 } ( x - 11 ) ^ { 2 }$ 
B)  $f ( x ) = ( x + 5 ) ( x - 11 ) ( x - 5 ) ( x + 11 )$ 
C)  $f ( x ) = ( x + 5 ) ( x - 11 )$ 
D)  $f ( x ) = ( x - 5 ) ^ { 2 } ( x + 11 ) ^ { 2 }$

Question 8

Solve the inequality.
-$$\frac { 9 } { x + 9 } > \frac { 8 } { x + 9 }$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 9 )$ 
C)  $( - 9 , \infty )$ 
D)  $\varnothing$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 9 )$ 
C)  $( - 9 , \infty )$ 
D)  $\varnothing$

Question 9

Find a cubic function with the given zeros.
-$$- 4,5 , - 3$$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 23 x - 60$ 
B)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 23 x + 60$ 
C)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 23 x - 60$ 
D)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 23 x - 60$ 
A)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 23 x - 60$ 
B)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 23 x + 60$ 
C)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 23 x - 60$ 
D)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 23 x - 60$

Question 10

Solve the problem.
-Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows:
$S ( p ) = 200 - 2 p + 0.00001 p ^ { 4 }$ and $D ( p ) = 1400 - 0.0006 p ^ { 3 }$, where $p$ is the price. Determine the price for which the supply equals the demand.

Accepted Answer

A)  $\$ 96.24$ 
B)  $\$ 100.24$ 
C)  $\$ 93.24$ 
D)  $\$ 99.24$ 
A)  $\$ 96.24$ 
B)  $\$ 100.24$ 
C)  $\$ 93.24$ 
D)  $\$ 99.24$

Question 11

Write a linear factorization of the function.
-$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 2 x - 5$

Accepted Answer

A)  $f ( x ) = ( x - 1 ) ( 2 x + 3 + \sqrt { 11 } i ) ( 2 x + 3 - \sqrt { 11 } i )$ 
B)  $f ( x ) = ( x + 1 ) ( 2 x + 3 + \sqrt { 7 } i ) ( 2 x + 3 - \sqrt { 7 } i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 3 + \sqrt { 11 } i ) ( x + 3 - \sqrt { 11 } i )$ 
D)  $f ( x ) = ( x + 1 ) ( 2 x + 3 + \sqrt { 11 } i ) ( 2 x + 3 - \sqrt { 11 } i )$ 
A)  $f ( x ) = ( x - 1 ) ( 2 x + 3 + \sqrt { 11 } i ) ( 2 x + 3 - \sqrt { 11 } i )$ 
B)  $f ( x ) = ( x + 1 ) ( 2 x + 3 + \sqrt { 7 } i ) ( 2 x + 3 - \sqrt { 7 } i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 3 + \sqrt { 11 } i ) ( x + 3 - \sqrt { 11 } i )$ 
D)  $f ( x ) = ( x + 1 ) ( 2 x + 3 + \sqrt { 11 } i ) ( 2 x + 3 - \sqrt { 11 } i )$

Question 12

Graph the function in a viewing window that shows all of its extrema and x-intercepts.
-$$f ( x ) = ( x + 1 ) ( x + 3 ) ( x - 1 )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 13

Write a linear factorization of the function.
-$$f ( x ) = x ^ { 2 } + 3$$

Accepted Answer

A)  $f ( x ) = ( x + \sqrt { 3 } ) ( x + i \sqrt { 3 } )$ 
B)  $f ( x ) = ( x + \sqrt { 3 } ) ^ { 2 }$ 
C)  $f ( x ) = ( x + i \sqrt { 3 } ) ( x - i \sqrt { 3 } )$ 
D)  $f ( x ) = ( x + i \sqrt { 3 } ) ^ { 2 }$ 
A)  $f ( x ) = ( x + \sqrt { 3 } ) ( x + i \sqrt { 3 } )$ 
B)  $f ( x ) = ( x + \sqrt { 3 } ) ^ { 2 }$ 
C)  $f ( x ) = ( x + i \sqrt { 3 } ) ( x - i \sqrt { 3 } )$ 
D)  $f ( x ) = ( x + i \sqrt { 3 } ) ^ { 2 }$

Question 14

Choose the one alternative that best completes the statement or answers the question.
Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n.
-$$f ( x ) = 9 x ^ { 3 }$$

Accepted Answer

A)  Vertically stretch by a factor of 9 
B)  Horizontally stretch by a factor of 9 
C)  Horizontally stretch by a factor of 9 , and then reflect across $x$-axis 
D)  Vertically stretch by a factor of 9 , and then reflect across $x$-axis 
A)  Vertically stretch by a factor of 9 
B)  Horizontally stretch by a factor of 9 
C)  Horizontally stretch by a factor of 9 , and then reflect across $x$-axis 
D)  Vertically stretch by a factor of 9 , and then reflect across $x$-axis

Question 15

Write a linear factorization of the function.
-$$f ( x ) = x ^ { 4 } - 18 x ^ { 3 } + 82 x ^ { 2 } - 18 x + 81$$

Accepted Answer

A)  $f ( x ) = ( x - 9 ) ^ { 2 } ( x + i ) ( x - i )$ 
B)  $f ( x ) = ( x - 9 ) ( x - 8 ) ( x + i ) ( x - i )$ 
C)  $f ( x ) = ( x - 9 ) ( x - 7 ) ( x + i ) ( x - i )$ 
D)  $f ( x ) = ( x - 9 ) ( x + i ) ( x - i )$ 
A)  $f ( x ) = ( x - 9 ) ^ { 2 } ( x + i ) ( x - i )$ 
B)  $f ( x ) = ( x - 9 ) ( x - 8 ) ( x + i ) ( x - i )$ 
C)  $f ( x ) = ( x - 9 ) ( x - 7 ) ( x + i ) ( x - i )$ 
D)  $f ( x ) = ( x - 9 ) ( x + i ) ( x - i )$

Question 16

Solve the problem.
-The Cool Company determines that the supply function for its basic air conditioning unit is $S ( p ) = 10 + 0.002 p ^ { 3 }$ and that its demand function is $D ( p ) = 50 - 0.04 p ^ { 2 }$, where $p$ is the price. Determine the price for which the supply equals the demand.

Accepted Answer

A)  $\$ 21.36$ 
B)  $\$ 22.36$ 
C)  $\$ 21.86$ 
D)  $\$ 22.86$ 
A)  $\$ 21.36$ 
B)  $\$ 22.36$ 
C)  $\$ 21.86$ 
D)  $\$ 22.86$

Question 17

Solve the inequality.
-$\frac { x ^ { 2 } ( x - 1 ) ^ { 3 } } { \sqrt { x + 7 } } < 0$

Accepted Answer

A)  $( - 7 , \infty )$ 
B)  $( - 7,0 ) \cup ( 0,1 )$ 
C)  $( - 7,0 ) \cup ( 1 , \infty )$ 
D)  $( - 7,0 ) \cup ( 0 , \infty )$ 
A)  $( - 7 , \infty )$ 
B)  $( - 7,0 ) \cup ( 0,1 )$ 
C)  $( - 7,0 ) \cup ( 1 , \infty )$ 
D)  $( - 7,0 ) \cup ( 0 , \infty )$

Question 18

Solve the problem.
-The population $\mathrm { P }$, in thousands, of Jonesburg is given by
$$P ( t ) = \frac { 500 t } { 2 t ^ { 2 } + 8 }$$
where $t$ is the time, in months.
Graph the function on the interval $[ 0 , \infty )$ and complete the following: $\mathrm { P } ( \mathrm { t } ) \rightarrow \quad$ as $\mathrm { t } \rightarrow \infty $

Accepted Answer

A) 
 
$\mathrm { P } ( \mathrm { t } ) \rightarrow 50$ as $t \rightarrow \infty$. 
B)

$\mathrm { P } ( \mathrm { t } ) \rightarrow 1$ as $t \rightarrow \infty .$ 
C) 
 
$\mathrm { P } ( \mathrm { t } ) \rightarrow 0$ as $\mathrm { t } \rightarrow \infty $ 
D) 
 
$P ( t ) \rightarrow 45$ as $t \rightarrow \infty$. 
A) 
 
$\mathrm { P } ( \mathrm { t } ) \rightarrow 50$ as $t \rightarrow \infty$. 
B)

$\mathrm { P } ( \mathrm { t } ) \rightarrow 1$ as $t \rightarrow \infty .$ 
C) 
 
$\mathrm { P } ( \mathrm { t } ) \rightarrow 0$ as $\mathrm { t } \rightarrow \infty $ 
D) 
 
$P ( t ) \rightarrow 45$ as $t \rightarrow \infty$.

Question 19

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
-$$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 2 x ^ { 2 } + 36 x - 48$$

Accepted Answer

A)  4 (rational), 2 (rational), $\sqrt { 6 }$ (irrational), and $- \sqrt { 6 }$ (irrational) 
B)  $- 4$ (rational), $- 2$ (rational), $2 + \sqrt { 6 }$ (irrational), and $2 - \sqrt { 6 }$ (irrational) 
C)  $- 4$ (rational), $- 2$ (rational), $\sqrt { 6 }$ (irrational), and $- \sqrt { 6 }$ (irrational) 
D)  4 (rational), 2 (rational), $2 + \sqrt { 6 }$ (irrational), and $2 - \sqrt { 6 }$ (irrational) 
A)  4 (rational), 2 (rational), $\sqrt { 6 }$ (irrational), and $- \sqrt { 6 }$ (irrational) 
B)  $- 4$ (rational), $- 2$ (rational), $2 + \sqrt { 6 }$ (irrational), and $2 - \sqrt { 6 }$ (irrational) 
C)  $- 4$ (rational), $- 2$ (rational), $\sqrt { 6 }$ (irrational), and $- \sqrt { 6 }$ (irrational) 
D)  4 (rational), 2 (rational), $2 + \sqrt { 6 }$ (irrational), and $2 - \sqrt { 6 }$ (irrational)

Question 20

State how many complex and real zeros the function has.
-$$f ( x ) = x ^ { 5 } - 8 x ^ { 4 } + 2 x ^ { 3 } - 16 x ^ { 2 } + x - 8$$

Accepted Answer

A)  5 complex zeros; 3 real 
B)  5 complex zeros; all 5 real 
C)  5 complex zeros; 1 real 
D)  5 complex zeros; none real 
A)  5 complex zeros; 3 real 
B)  5 complex zeros; all 5 real 
C)  5 complex zeros; 1 real 
D)  5 complex zeros; none real

Find the vertex of the graph of the function. - $f ( x ) = 4 x ^ { 2 } + 16 x + 21$

Write an equation for the linear function f satisfying the given conditions. - $f ( - 3 ) = 8$ and $f ( 1 ) = 4$

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - $f ( x ) = \left( 2 x ^ { 2 } + 3 \right) ( x - 6 ) ^ { 2 } ( x + 9 ) ^ { 3 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros: $- 3 , - 1,4 ; f ( 2 ) = 10$

Solve the problem. Round as appropriate. -The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2.5 sec when the length is 25 inches, what is the period when L = 3.0625 inches?

Provide an appropriate response. -Suppose that $\mathrm { f }$ is a polynomial function of degree 4 . If $- 5$ and 11 are zeros of $f$ and the graph of $f$ is symmetric with respect to the $y$ -axis, write $f ( x )$ in factored form.

Solve the inequality. - $\frac { 9 } { x + 9 } > \frac { 8 } { x + 9 }$

Find a cubic function with the given zeros. - $- 4,5 , - 3$

Write a linear factorization of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 2 x - 5$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = ( x + 1 ) ( x + 3 ) ( x - 1 )$

Write a linear factorization of the function. - $f ( x ) = x ^ { 2 } + 3$

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = 9 x ^ { 3 }$

Write a linear factorization of the function. - $f ( x ) = x ^ { 4 } - 18 x ^ { 3 } + 82 x ^ { 2 } - 18 x + 81$

Solve the problem. -The Cool Company determines that the supply function for its basic air conditioning unit is $S ( p ) = 10 + 0.002 p ^ { 3 }$ and that its demand function is $D ( p ) = 50 - 0.04 p ^ { 2 }$ , where $p$ is the price. Determine the price for which the supply equals the demand.

Solve the inequality. - $\frac { x ^ { 2 } ( x - 1 ) ^ { 3 } } { \sqrt { x + 7 } } < 0$

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 2 x ^ { 2 } + 36 x - 48$

State how many complex and real zeros the function has. - $f ( x ) = x ^ { 5 } - 8 x ^ { 4 } + 2 x ^ { 3 } - 16 x ^ { 2 } + x - 8$

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 vertex of the graph of the function. - f(x)=4x2+16x+21f ( x ) = 4 x ^ { 2 } + 16 x + 21f(x)=4x2+16x+21

Write an equation for the linear function f satisfying the given conditions. - f(−3)=8f ( - 3 ) = 8f(−3)=8 and f(1)=4f ( 1 ) = 4f(1)=4

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - f(x)=(2x2+3)(x−6)2(x+9)3f ( x ) = \left( 2 x ^ { 2 } + 3 \right) ( x - 6 ) ^ { 2 } ( x + 9 ) ^ { 3 }f(x)=(2x2+3)(x−6)2(x+9)3

Describe how to transform the graph of an appropriate monomial function f(x) = xn into the graph of the given polynomial function. Then sketch the transformed graph. - g(x)=−(x+2)3g ( x ) = - ( x + 2 ) ^ { 3 }g(x)=−(x+2)3

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros: −3,−1,4;f(2)=10- 3 , - 1,4 ; f ( 2 ) = 10−3,−1,4;f(2)=10