Question 1

Find all rational zeros and factor f(x).
-$$f ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } - x + 3$$

Accepted Answer

A)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 3 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 3 )$ 
B)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 3 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 3 )$ 
C)  $2 , - 2,3 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 3 )$ 
D)  $1 , - 1,3 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 3 )$ 
A)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 3 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 3 )$ 
B)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 3 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 3 )$ 
C)  $2 , - 2,3 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 3 )$ 
D)  $1 , - 1,3 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 3 )$

Question 2

Identify the vertex of the parabola.
-$$y = x ^ { 2 } + 4$$

Accepted Answer

A)  $( 4,0 )$ 
B) $( - 4,0 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0,4 )$ 
A)  $( 4,0 )$ 
B) $( - 4,0 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0,4 )$

Question 3

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=-2(x-3)^{2}+2$
 
 Find the $x$-intercepts.

Accepted Answer

A)  $( 1,0 )$ and $( 5,0 )$ 
B)  $( 0,2 )$ and $( 0,4 )$ 
C)  $( 2,0 )$ and $( 4,0 )$ 
D)  $( - 3,0 )$ and $( 3,0 )$ 
A)  $( 1,0 )$ and $( 5,0 )$ 
B)  $( 0,2 )$ and $( 0,4 )$ 
C)  $( 2,0 )$ and $( 4,0 )$ 
D)  $( - 3,0 )$ and $( 3,0 )$

Question 4

Find an equation for the rational function graph.
-In the following formula, $\mathrm { f } ( \mathrm { x } )$ is the minimum number of hours of studying required to attain a test score of $x : f ( x ) = \frac { 0.48 x } { 100.5 - x }$. How many hours of study are needed to score $85 ?$

Accepted Answer

A)  $26.30 \mathrm { hr }$ 
B)  $2.63 \mathrm { hr }$ 
C)  $100.93 \mathrm { hr }$ 
D)  $5.18 \mathrm { hr }$ 
A)  $26.30 \mathrm { hr }$ 
B)  $2.63 \mathrm { hr }$ 
C)  $100.93 \mathrm { hr }$ 
D)  $5.18 \mathrm { hr }$

Question 5

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32$$

Accepted Answer

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

Question 6

Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$-intercepts?

Accepted Answer

A)  $a > \frac { 4 } { 5 }$ 
B)  $\mathrm { a }  \frac { 16 } { 5 }$ 
A)  $a > \frac { 4 } { 5 }$ 
B)  $\mathrm { a }  \frac { 16 } { 5 }$

Question 7

Identify the vertex of the parabola.
-$$y = 3 x ^ { 2 } + 24 x + 49$$

Accepted Answer

A)  $( 1 , - 4 )$ 
B)  $( 4 , - 1 )$ 
C)  $( - 4,1 )$ 
D)  $( - 1,4 )$ 
A)  $( 1 , - 4 )$ 
B)  $( 4 , - 1 )$ 
C)  $( - 4,1 )$ 
D)  $( - 1,4 )$

Question 8

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 4 - 4 x + x ^ { 2 } - x ^ { 3 } - 4 x ^ { 4 }$$

Accepted Answer

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

Question 9

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 17$ 
B)  $\pm 1 , \pm 2 , \pm 17 , \pm \frac { 17 } { 2 }$ 
C)  $\pm 1 , \pm \frac { 1 } { 17 } , \pm 2 , \pm \frac { 2 } { 17 }$ 
D)  $\pm 1 , \pm 17 , \pm \frac { 1 } { 2 } , \pm \frac { 17 } { 2 }$ 
A)  $\pm 1 , \pm 2 , \pm 17$ 
B)  $\pm 1 , \pm 2 , \pm 17 , \pm \frac { 17 } { 2 }$ 
C)  $\pm 1 , \pm \frac { 1 } { 17 } , \pm 2 , \pm \frac { 2 } { 17 }$ 
D)  $\pm 1 , \pm 17 , \pm \frac { 1 } { 2 } , \pm \frac { 17 } { 2 }$

Question 10

Solve the problem
-$$\begin{array} { c | c } 
\text { Year } & \text { \# of Students } \
\hline 1960 & 190 \
1970 & 200 \
1980 & 230 \
1990 & 280 \
2000 & 350 \
2010 & 440
\end{array}$$ Take 1910 as year zero, and determine the linear or quadratic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 5 x - 93.2$ 
B)  $f ( x ) = 0.1 x ^ { 2 } - 10 x + 440$ 
C)  $f ( x ) = 0.16 x ^ { 2 } - 17.5 x + 106$ 
D)  $f ( x ) = 0.27 x ^ { 2 } - 29.1 x - 410$ 
A)  $f ( x ) = 5 x - 93.2$ 
B)  $f ( x ) = 0.1 x ^ { 2 } - 10 x + 440$ 
C)  $f ( x ) = 0.16 x ^ { 2 } - 17.5 x + 106$ 
D)  $f ( x ) = 0.27 x ^ { 2 } - 29.1 x - 410$

Question 11

Translate the given formula to an English phrase using the word "varies".
-$\mathrm { I } = \mathrm { PRT }$, where $\mathrm { I }$ is the simple interest on a principal of $\mathrm { P }$ dollars invested for $\mathrm { T }$ years at an interest rate of $\mathrm { R }$ per year

Accepted Answer

Simple interest vari

Question 12

Match the equation to the correct graph.
-$$y = ( x + 2 ) ^ { 2 }$$

Accepted Answer

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

Question 13

Solve the problem
-If an object is propelled upward from a height of 112 feet at an initial velocity of 96 feet per second, then its height after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 96 t + 112$. After how many seconds does the object hit the ground?

Accepted Answer

A)  $6.0 \mathrm { sec }$ 
B)  $3.5 \mathrm { sec }$ 
C)  $7 \mathrm { sec }$ 
D)  $11 \mathrm { sec }$ 
A)  $6.0 \mathrm { sec }$ 
B)  $3.5 \mathrm { sec }$ 
C)  $7 \mathrm { sec }$ 
D)  $11 \mathrm { sec }$

Question 14

Give the equations of any vertical asymptotes.
-$$g ( x ) = \frac { x - 7 } { ( x - 3 ) ( x + 6 ) }$$

Accepted Answer

A)  $x = 3 , x = - 6$ 
B)  $x = 7$ 
C)  $x = - 7$ 
D)  $x = - 3 , x = 6$ 
A)  $x = 3 , x = - 6$ 
B)  $x = 7$ 
C)  $x = - 7$ 
D)  $x = - 3 , x = 6$

Question 15

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 5 x ( x + 6 ) \left( x ^ { 2 } - 16 \right) ^ { 2 }$$

Accepted Answer

A)  0 (multiplicity 1), $- 6$ (multiplicity $1 ), \pm 4$ (multiplicity 1 ) 
B)  0 (multiplicity 1), $- 6$ (multiplicity 1), - 16 (multiplicity 2) 
C)  0 (multiplicity 1), $- 6$ (multiplicity 1), $\pm 4$ (multiplicity 2 ) 
D)  0 (multiplicity 1), 6 (multiplicity 1), $\pm 4$ (multiplicity 2) 
A)  0 (multiplicity 1), $- 6$ (multiplicity $1 ), \pm 4$ (multiplicity 1 ) 
B)  0 (multiplicity 1), $- 6$ (multiplicity 1), - 16 (multiplicity 2) 
C)  0 (multiplicity 1), $- 6$ (multiplicity 1), $\pm 4$ (multiplicity 2 ) 
D)  0 (multiplicity 1), 6 (multiplicity 1), $\pm 4$ (multiplicity 2)

Question 16

Round to the nearest tenth unless indicated otherwise.
-The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$. If $\mathrm { V } = 400.0 \mathrm { in } ^ { 3 }$ when $\mathrm { T } = 400 ^ { \circ }$ and $\mathrm { P } = 15 \mathrm { lb } / \mathrm { in } ^ { 2 }$, what is the volume when $\mathrm { T } = 100 ^ { \circ }$ and $\mathrm { P } = 15 \mathrm { lb } / \mathrm { in } ^ { 2 } ?$

Accepted Answer

A)  $130.0$ in $^ { 3 }$ 
B)  $100.0 \mathrm { in } ^ { 3 }$ 
C)  $60.0$ in $^ { 3 }$ 
D)  $90.0 \mathrm { in } ^ { 3 }$ 
A)  $130.0$ in $^ { 3 }$ 
B)  $100.0 \mathrm { in } ^ { 3 }$ 
C)  $60.0$ in $^ { 3 }$ 
D)  $90.0 \mathrm { in } ^ { 3 }$

Question 17

Find the equation of the axis of symmetry of the parabola.
-$$f ( x ) = ( x - 5 ) ^ { 2 } - 5$$

Accepted Answer

A)  $y = - 5$ 
B)  $x = 5$ 
C)  $x = - 5$ 
D)  $y = 0$ 
A)  $y = - 5$ 
B)  $x = 5$ 
C)  $x = - 5$ 
D)  $y = 0$

Question 18

Find all rational zeros and factor f(x).
-$$f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } - 29 x + 5$$

Accepted Answer

A)  $2,4 , - 5 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 5 )$ 
B)  $\frac { 1 } { 8 } , 4 , - 5 ; f ( x ) = ( 8 x - 1 ) ( x - 4 ) ( x + 5 )$ 
C)  $\frac { 1 } { 2 } , \frac { 1 } { 4 } , - 5 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 5 )$ 
D)  $\frac { 1 } { 8 } , 1 , - 5 ; f ( x ) = ( 8 x - 1 ) ( x - 1 ) ( x + 5 )$ 
A)  $2,4 , - 5 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 5 )$ 
B)  $\frac { 1 } { 8 } , 4 , - 5 ; f ( x ) = ( 8 x - 1 ) ( x - 4 ) ( x + 5 )$ 
C)  $\frac { 1 } { 2 } , \frac { 1 } { 4 } , - 5 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 5 )$ 
D)  $\frac { 1 } { 8 } , 1 , - 5 ; f ( x ) = ( 8 x - 1 ) ( x - 1 ) ( x + 5 )$

Question 19

Round your answer to two decimal places.
-Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 25 pounds stretches a certain spring 7 inches, then how much
Will a force of 75 pounds stretch the spring?

Accepted Answer

A)  3 in. 
B)  175 in. 
C)  2 in. 
D)  21 in. 
A)  3 in. 
B)  175 in. 
C)  2 in. 
D)  21 in.

Question 20

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = - \frac { 9 } { ( x - 8 ) ^ { 2 } }$$

Accepted Answer

A)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 9 )$ 
B)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( 0 , \infty )$ 
C)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 )$ 
D)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 0 )$ 
A)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 9 )$ 
B)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( 0 , \infty )$ 
C)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 )$ 
D)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 0 )$

Find all rational zeros and factor f(x). - $f ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } - x + 3$

Identify the vertex of the parabola. - $y = x ^ { 2 } + 4$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-3)^{2}+2$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-3)^{2}+2 Find the x -intercepts.$ Find the $x$ -intercepts.

Find an equation for the rational function graph. -In the following formula, $\mathrm { f } ( \mathrm { x } )$ is the minimum number of hours of studying required to attain a test score of $x : f ( x ) = \frac { 0.48 x } { 100.5 - x }$ . How many hours of study are needed to score $85 ?$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Identify the vertex of the parabola. - $y = 3 x ^ { 2 } + 24 x + 49$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 4 - 4 x + x ^ { 2 } - x ^ { 3 } - 4 x ^ { 4 }$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17$

Solve the problem - Year \# of Students 1960 190 1970 200 1980 230 1990 280 2000 350 2010 440 Take 1910 as year zero, and determine the linear or quadratic function that best fits the data.

Translate the given formula to an English phrase using the word "varies". - $\mathrm { I } = \mathrm { PRT }$ , where $\mathrm { I }$ is the simple interest on a principal of $\mathrm { P }$ dollars invested for $\mathrm { T }$ years at an interest rate of $\mathrm { R }$ per year

Match the equation to the correct graph. - $y = ( x + 2 ) ^ { 2 }$

Solve the problem -If an object is propelled upward from a height of 112 feet at an initial velocity of 96 feet per second, then its height after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 96 t + 112$ . After how many seconds does the object hit the ground?

Give the equations of any vertical asymptotes. - $g ( x ) = \frac { x - 7 } { ( x - 3 ) ( x + 6 ) }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 5 x ( x + 6 ) \left( x ^ { 2 } - 16 \right) ^ { 2 }$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x - 5 ) ^ { 2 } - 5$

Find all rational zeros and factor f(x). - $f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } - 29 x + 5$

Round your answer to two decimal places. -Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 25 pounds stretches a certain spring 7 inches, then how much Will a force of 75 pounds stretch the spring?

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 9 } { ( x - 8 ) ^ { 2 } }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 4: Polynomial and Rational Functions

Find all rational zeros and factor f(x). - f(x)=4x3−12x2−x+3f ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } - x + 3f(x)=4x3−12x2−x+3

Identify the vertex of the parabola. - y=x2+4y = x ^ { 2 } + 4y=x2+4

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=−2(x−3)2+2f(x)=-2(x-3)^{2}+2f(x)=−2(x−3)2+2 Find the xxx -intercepts.

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=3x4−10x3+20x2−40x+32f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32f(x)=3x4−10x3+20x2−40x+32

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2+4x+5f ( x ) = a x ^ { 2 } + 4 x + 5f(x)=ax2+4x+5 have two xxx -intercepts?

Identify the vertex of the parabola. - y=3x2+24x+49y = 3 x ^ { 2 } + 24 x + 49y=3x2+24x+49

Find the correct end behavior diagram for the given polynomial function. - P(x)=4−4x+x2−x3−4x4P ( x ) = 4 - 4 x + x ^ { 2 } - x ^ { 3 } - 4 x ^ { 4 }P(x)=4−4x+x2−x3−4x4

Give all possible rational zeros for the following polynomial. - P(x)=2x3−5x2+7x−17P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17P(x)=2x3−5x2+7x−17