Question 1

Sketch the graph of the parabola.
-$y=x^{2}-2 x-9$

Accepted Answer

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

Question 2

Give the equations of any vertical asymptotes.
-$$h ( x ) = \frac { 3 x - 1 } { x ^ { 2 } + 3 x - 54 }$$

Accepted Answer

A)  $y = 3$ 
B)  $x = - 6 , x = 9$ 
C)  $x = 6 , x = - 9$ 
D)  $y = 6 , y = - 9$ 
A)  $y = 3$ 
B)  $x = - 6 , x = 9$ 
C)  $x = 6 , x = - 9$ 
D)  $y = 6 , y = - 9$

Question 3

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 3.9 x ^ { 4 } + 3 x ^ { 2 } + x - 2$$

Accepted Answer

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

Question 4

Find the domain and range of the function.
-$$f ( x ) = x ^ { 2 } + 16 x + 60$$

Accepted Answer

A)  Domain: $[ - 4 , \infty )$; Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ - 4 , \infty )$ 
C)  Domain: $[ - 4 , \infty )$; Range: $( - \infty , - 8 ]$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ - 8 , \infty )$ 
A)  Domain: $[ - 4 , \infty )$; Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ - 4 , \infty )$ 
C)  Domain: $[ - 4 , \infty )$; Range: $( - \infty , - 8 ]$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ - 8 , \infty )$

Question 5

Factor f(x) into linear factors given that k is a zero of f(x).
-$f ( x ) = 3 x ^ { 3 } + ( 5 - 3 i ) x ^ { 2 } + ( - 11 - 8 i ) x + 3 + 3 i ; k = 1 + i$

Accepted Answer

A)  $( x + ( 1 + i ) ) ( x - 3 ) ( 3 x + 1 )$ 
B)  $( x - ( 1 + i ) ) ( x + 2 ) ( 3 x - 1 )$ 
C)  $( x - ( 1 + i ) ) ( x - 3 ) ( 3 x + 1 )$ 
D)  $( x - ( 1 + i ) ) ( x + 3 ) ( 3 x - 1 )$ 
A)  $( x + ( 1 + i ) ) ( x - 3 ) ( 3 x + 1 )$ 
B)  $( x - ( 1 + i ) ) ( x + 2 ) ( 3 x - 1 )$ 
C)  $( x - ( 1 + i ) ) ( x - 3 ) ( 3 x + 1 )$ 
D)  $( x - ( 1 + i ) ) ( x + 3 ) ( 3 x - 1 )$

Question 6

Solve the problem.
-John owns a hot dog stand. He has found that his profit is represented by the equation $P ( x ) = - x ^ { 2 } + 56 x + 71$, with $P$ being profits and $x$ the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Accepted Answer

A)  43 hot dogs 
B)  21 hot dogs 
C)  29 hot dogs 
D)  28 hot dogs 
A)  43 hot dogs 
B)  21 hot dogs 
C)  29 hot dogs 
D)  28 hot dogs

Question 7

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope
positive or negative. If quadratic, decide whether the leading coefficient a of xS1U1P12S1S1P0 should be positive or negative.
-The height of a bouncing ball during one bounce, as a function of time.

Accepted Answer

A)  linear; negative 
B)  quadratic; positive 
C)  linear; positive 
D)  quadratic; negative 
A)  linear; negative 
B)  quadratic; positive 
C)  linear; positive 
D)  quadratic; negative

Question 8

Solve the problem.
-If $\mathrm { m }$ varies directly as $\mathrm { x }$ and $\mathrm { y }$, and $\mathrm { m } = 24$ when $\mathrm { x } = 6$ and $\mathrm { y } = 9$, find $\mathrm { m }$ when $\mathrm { x } = 15$ and $\mathrm { y } = 8$.

Accepted Answer

A)  $\frac { 140 } { 3 }$ 
B)  $\frac { 64 } { 3 }$ 
C)  $\frac { 160 } { 3 }$ 
D)  60 
A)  $\frac { 140 } { 3 }$ 
B)  $\frac { 64 } { 3 }$ 
C)  $\frac { 160 } { 3 }$ 
D)  60

Question 9

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 18 x + 20$$

Accepted Answer

A)  $1 + i , 1 - i , - 10$ 
B)  $1 + i , - 10,10$ 
C)  $1 + i , 1 - i , 10$ 
D)  $1 + \mathrm { i } , 1 - \mathrm { i } , 10 \mathrm { i }$ 
A)  $1 + i , 1 - i , - 10$ 
B)  $1 + i , - 10,10$ 
C)  $1 + i , 1 - i , 10$ 
D)  $1 + \mathrm { i } , 1 - \mathrm { i } , 10 \mathrm { i }$

Question 10

Solve the problem.
-$A ( x ) = - 0.015 x ^ { 3 } + 1.05 x$ gives the alcohol level in an average person's blood $x$ hrs after drinking 8 oz of 100 -proof whiskey. If the level exceeds $1.5$ units, a person is legally drunk. Would a person be drunk after 2 hours?

Accepted Answer

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

Question 11

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; - 4$$

Accepted Answer

A)  $3 + 4 \mathrm { i } , 3 - 4 \mathrm { i }$ 
B)  $1 + 2 i , 1 - 2 i$ 
C)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$ 
D)  $3 + 2 i , 3 - 2 i$ 
A)  $3 + 4 \mathrm { i } , 3 - 4 \mathrm { i }$ 
B)  $1 + 2 i , 1 - 2 i$ 
C)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$ 
D)  $3 + 2 i , 3 - 2 i$

Question 12

Solve the problem. Round your answer to two decimal places.
-Hookeʹs Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 10 pounds stretches a certain spring 6 inches, then how
Much will a force of 30 pounds stretch the spring?

Accepted Answer

A)  3 in. 
B)  60 in. 
C)  18 in. 
D)  2 in. 
A)  3 in. 
B)  60 in. 
C)  18 in. 
D)  2 in.

Question 13

Find the zeros of the polynomial function and state the multiplicity of each.
-$$4 ( x + 4 ) ^ { 2 } ( x - 4 ) ( x - 2 + i )$$

Accepted Answer

A)  4 (multiplicity 2), 4 (multiplicity 1), 2 - i (multiplicity 1) 
B)  $- 4$ (multiplicity 2), 4 (multiplicity 1), 2 - i (multiplicity 1 ) 
C)  $- 4$ (multiplicity 2), $- 4$ (multiplicity 1), 2 - i (multiplicity 1 ) 
D)  4 (multiplicity 2), $- 4$ (multiplicity 1 ), $- 2 + \mathrm { i }$ (multiplicity 1 ) 
A)  4 (multiplicity 2), 4 (multiplicity 1), 2 - i (multiplicity 1) 
B)  $- 4$ (multiplicity 2), 4 (multiplicity 1), 2 - i (multiplicity 1 ) 
C)  $- 4$ (multiplicity 2), $- 4$ (multiplicity 1), 2 - i (multiplicity 1 ) 
D)  4 (multiplicity 2), $- 4$ (multiplicity 1 ), $- 2 + \mathrm { i }$ (multiplicity 1 )

Question 14

Identify the vertex of the parabola.
-$$f ( x ) = ( x - 7 ) ^ { 2 } - 5$$

Accepted Answer

A)  $( 7 , - 5 )$ 
B)  $( - 5,7 )$ 
C)  $( - 5,0 )$ 
D)  $( 0,7 )$ 
A)  $( 7 , - 5 )$ 
B)  $( - 5,7 )$ 
C)  $( - 5,0 )$ 
D)  $( 0,7 )$

Question 15

Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$-intercept?

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  9 
C)  24 
D)  $- 9$ 
A)  $\frac { 3 } { 2 }$ 
B)  9 
C)  24 
D)  $- 9$

Question 16

Find a polynomial function f(x) of least possible degree having the graph shown.
-

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 3 ) ( x - 1 ) ( x - 4 )$ 
C)  $f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ( x - 1 ) ( x - 4 )$ 
D)  $f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ( x + 1 ) ( x + 4 )$ 
A)  $f ( x ) = ( x + 3 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 3 ) ( x - 1 ) ( x - 4 )$ 
C)  $f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ( x - 1 ) ( x - 4 )$ 
D)  $f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ( x + 1 ) ( x + 4 )$

Question 17

Provide an appropriate response.
-What is the range of the graph?

Accepted Answer

A)  $( - 8.85 , \infty )$ 
B)  $( - 8.85,44.86 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 3.43,8.61 )$ 
A)  $( - 8.85 , \infty )$ 
B)  $( - 8.85,44.86 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 3.43,8.61 )$

Question 18

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$$\text { 3; } f ( x ) = - x ^ { 4 } + 8 x ^ { 2 } - x + 5$$

Accepted Answer

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

Question 19

Solve the problem.
-The graph of $f ( x ) = x ^ { 3 } - x ^ { 2 } - 8 x + 12$ is shown below. Use the graph to factor $f ( x )$.

Accepted Answer

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

Question 20

Give the equations of any vertical asymptotes.
-$h ( x ) = \frac { ( x - 6 ) ( x + 3 ) } { x ^ { 2 } - 1 }$

Accepted Answer

A)  $x = 6 , x = - 3$ 
B)  $x = - 6 , x = 3$ 
C)  $x = 1 , x = - 1$ 
D)  none 
A)  $x = 6 , x = - 3$ 
B)  $x = - 6 , x = 3$ 
C)  $x = 1 , x = - 1$ 
D)  none

Sketch the graph of the parabola. - $y=x^{2}-2 x-9$ $Sketch the graph of the parabola. - y=x^{2}-2 x-9$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 3 x - 1 } { x ^ { 2 } + 3 x - 54 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 3.9 x ^ { 4 } + 3 x ^ { 2 } + x - 2$

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } + 16 x + 60$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 3 x ^ { 3 } + ( 5 - 3 i ) x ^ { 2 } + ( - 11 - 8 i ) x + 3 + 3 i ; k = 1 + i$

Solve the problem. -John owns a hot dog stand. He has found that his profit is represented by the equation $P ( x ) = - x ^ { 2 } + 56 x + 71$ , with $P$ being profits and $x$ the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -The height of a bouncing ball during one bounce, as a function of time.

Solve the problem. -If $\mathrm { m }$ varies directly as $\mathrm { x }$ and $\mathrm { y }$ , and $\mathrm { m } = 24$ when $\mathrm { x } = 6$ and $\mathrm { y } = 9$ , find $\mathrm { m }$ when $\mathrm { x } = 15$ and $\mathrm { y } = 8$ .

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 18 x + 20$

Solve the problem. - $A ( x ) = - 0.015 x ^ { 3 } + 1.05 x$ gives the alcohol level in an average person's blood $x$ hrs after drinking 8 oz of 100 -proof whiskey. If the level exceeds $1.5$ units, a person is legally drunk. Would a person be drunk after 2 hours?

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; - 4$

Solve the problem. Round your answer to two decimal places. -Hookeʹs Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 10 pounds stretches a certain spring 6 inches, then how Much will a force of 30 pounds stretch the spring?

Find the zeros of the polynomial function and state the multiplicity of each. - $4 ( x + 4 ) ^ { 2 } ( x - 4 ) ( x - 2 + i )$

Identify the vertex of the parabola. - $f ( x ) = ( x - 7 ) ^ { 2 } - 5$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Find a polynomial function f(x) of least possible degree having the graph shown. -

Provide an appropriate response. -What is the range of the graph?

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $\text { 3; } f ( x ) = - x ^ { 4 } + 8 x ^ { 2 } - x + 5$

Solve the problem. -The graph of $f ( x ) = x ^ { 3 } - x ^ { 2 } - 8 x + 12$ is shown below. Use the graph to factor $f ( x )$ . $Solve the problem. -The graph of f ( x ) = x ^ { 3 } - x ^ { 2 } - 8 x + 12 is shown below. Use the graph to factor f ( x ) .$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { ( x - 6 ) ( x + 3 ) } { x ^ { 2 } - 1 }$

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

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Sketch the graph of the parabola. - y=x2−2x−9y=x^{2}-2 x-9y=x2−2x−9

Give the equations of any vertical asymptotes. - h(x)=3x−1x2+3x−54h ( x ) = \frac { 3 x - 1 } { x ^ { 2 } + 3 x - 54 }h(x)=x2+3x−543x−1​

Find the correct end behavior diagram for the given polynomial function. - P(x)=3.9x4+3x2+x−2P ( x ) = 3.9 x ^ { 4 } + 3 x ^ { 2 } + x - 2P(x)=3.9x4+3x2+x−2

Find the domain and range of the function. - f(x)=x2+16x+60f ( x ) = x ^ { 2 } + 16 x + 60f(x)=x2+16x+60

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=3x3+(5−3i)x2+(−11−8i)x+3+3i;k=1+if ( x ) = 3 x ^ { 3 } + ( 5 - 3 i ) x ^ { 2 } + ( - 11 - 8 i ) x + 3 + 3 i ; k = 1 + if(x)=3x3+(5−3i)x2+(−11−8i)x+3+3i;k=1+i

Solve the problem. -John owns a hot dog stand. He has found that his profit is represented by the equation P(x)=−x2+56x+71P ( x ) = - x ^ { 2 } + 56 x + 71P(x)=−x2+56x+71 , with PPP being profits and xxx the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x2 should be positive or negative. -The height of a bouncing ball during one bounce, as a function of time.

Solve the problem. -If m\mathrm { m }m varies directly as x\mathrm { x }x and y\mathrm { y }y , and m=24\mathrm { m } = 24m=24 when x=6\mathrm { x } = 6x=6 and y=9\mathrm { y } = 9y=9 , find m\mathrm { m }m when x=15\mathrm { x } = 15x=15 and y=8\mathrm { y } = 8y=8 .

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3+8x2−18x+20f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 18 x + 20f(x)=x3+8x2−18x+20

For the polynomial, one zero is given. Find all others. - P(x)=x3−2x2−11x+52;−4P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; - 4P(x)=x3−2x2−11x+52;−4