Question 1

Use synthetic division to perform the division.
-$$\frac { x ^ { 3 } + \frac { 5 } { 2 } x ^ { 2 } - 2 x - \frac { 3 } { 2 } } { x + \frac { 1 } { 2 } }$$

Accepted Answer

A)  $x ^ { 2 } + 2 x - 3$ 
B)  $x ^ { 2 } - \frac { 13 } { 2 } x + \frac { 7 } { 2 } - 2$ 
C)  $x ^ { 2 } - \frac { 13 } { 2 } x + \frac { - 2 } { x + 1 }$ 
D)  $x ^ { 2 } + 2 x - 6$ 
A)  $x ^ { 2 } + 2 x - 3$ 
B)  $x ^ { 2 } - \frac { 13 } { 2 } x + \frac { 7 } { 2 } - 2$ 
C)  $x ^ { 2 } - \frac { 13 } { 2 } x + \frac { - 2 } { x + 1 }$ 
D)  $x ^ { 2 } + 2 x - 6$

Question 2

Solve.
-The price of electric guitars has varied considerably in recent years. The data in the table relates the price P, in dollars, to time t, in years. Use a cubic function fitted to the data to predict the price of an electric guitar in
Year 10. $$\begin{array} { c | c } 
\text { Year, } \mathrm { t } & \begin{array} { c } 
\text { Average price, } \mathrm { p } , \
\text { of an electric guitar }
\end{array} \
\hline 1 & \$ 618.20 \
\hline 2 & 783.20 \
\hline 3 & 674.30 \
\hline 4 & 721.60 \
\hline 5 & 825.00 \
\hline 6 & 891.00 \
\hline 7 & 852.50 \
\hline 8 & 819.50 \
\hline 9 & 783.20
\end{array}$$

Accepted Answer

A)  $443.52 
B)  $893.53 
C)  $827.42 
D)  $670.48 
A)  $443.52 
B)  $893.53 
C)  $827.42 
D)  $670.48

Question 3

Solve.
-The data in the table show the number of burglaries reported in a small town for several years on record. $$\begin{array} { c | c } 
\text { Year } & \text { \# of Burglaries } \
\hline 0 & 8 \
2 & 5 \
4 & 6 \
6 & 3 \
7 & 3 \
8 & 2 \
11 & 2 \
13 & 3 \
15 & 3
\end{array}$$ Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 0.001 x ^ { 3 } + 0.03 x ^ { 2 } - 0.93 x + 7.78$ 
B)  $f ( x ) = - 0.0003 x ^ { 4 } + 0.01 x ^ { 3 } - 0.07 x ^ { 2 } - 0.65 x + 7.68$ 
C)  $f ( x ) = - 0.31 x + 6.15$ 
D)  $f ( x ) = 0.0003 x ^ { 3 } + 0.01 x ^ { 2 } - 0.07 x + 7.68$ 
A)  $f ( x ) = 0.001 x ^ { 3 } + 0.03 x ^ { 2 } - 0.93 x + 7.78$ 
B)  $f ( x ) = - 0.0003 x ^ { 4 } + 0.01 x ^ { 3 } - 0.07 x ^ { 2 } - 0.65 x + 7.68$ 
C)  $f ( x ) = - 0.31 x + 6.15$ 
D)  $f ( x ) = 0.0003 x ^ { 3 } + 0.01 x ^ { 2 } - 0.07 x + 7.68$

Question 4

Determine which of the rational functions given below has the following feature(s).
-The vertical asymptote is x = 5

Accepted Answer

A)  $f ( x ) = \frac { x - 5 } { x + 9 }$ 
B)  $f ( x ) = \frac { x + 9 } { x + 5 }$ 
C)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
D)  $f ( x ) = \frac { x + 9 } { x - 5 }$ 
A)  $f ( x ) = \frac { x - 5 } { x + 9 }$ 
B)  $f ( x ) = \frac { x + 9 } { x + 5 }$ 
C)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
D)  $f ( x ) = \frac { x + 9 } { x - 5 }$

Question 5

Provide an appropriate response.
-What are the possible number of real zeros (counting multiplicities) for a polynomial 
function with real coefficients of degree four?

Accepted Answer

The answer of Provide an appropriate response.
-What are the possible...

Question 6

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 13 , \pm \frac { 13 } { 2 } , \pm \frac { 1 } { 13 } , \pm \frac { 1 } { 26 }$ 
B)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm \frac { 2 } { 13 } , \pm 13 , \pm 26$ 
C)  $\pm 1 , \pm 2 , \pm 13 , \pm 26$ 
D)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm 13 , \pm 26$ 
A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 13 , \pm \frac { 13 } { 2 } , \pm \frac { 1 } { 13 } , \pm \frac { 1 } { 26 }$ 
B)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm \frac { 2 } { 13 } , \pm 13 , \pm 26$ 
C)  $\pm 1 , \pm 2 , \pm 13 , \pm 26$ 
D)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm 13 , \pm 26$

Question 7

Give the equations of any vertical asymptotes.
-$$h ( x ) = \frac { 5 } { x - 5 }$$

Accepted Answer

A)  $y = 5$ 
B)  none 
C)  $x = - 5$ 
D)  $x = 5$ 
A)  $y = 5$ 
B)  none 
C)  $x = - 5$ 
D)  $x = 5$

Question 8

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { - 4 } { x ^ { 2 } } \text { is symmetrical with respect to the } y \text {-axis. }$$

Accepted Answer

A) True 
 B)False

Question 9

Graph the function.
-$$f ( x ) = \frac { 7 } { x ^ { 2 } }$$

Accepted Answer

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

Question 10

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be
positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative.
-The amount of water in a pool as it is being filled, as a function of time.

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $x = 2$ 
B)  $y = 2$ 
C)  $x = - 2$ 
D)  $x = 0$ 
A)  $x = 2$ 
B)  $y = 2$ 
C)  $x = - 2$ 
D)  $x = 0$

Question 12

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { 2 } { x ^ { 2 } + 5 }$ 
B)  $f ( x ) = \frac { 2 } { x ^ { 2 } - 5 }$ 
C)  $f ( x ) = \frac { 2 } { x ^ { 2 } + 1 }$ 
D)  $f ( x ) = \frac { 2 } { x ^ { 2 } - 1 }$ 
A)  $f ( x ) = \frac { 2 } { x ^ { 2 } + 5 }$ 
B)  $f ( x ) = \frac { 2 } { x ^ { 2 } - 5 }$ 
C)  $f ( x ) = \frac { 2 } { x ^ { 2 } + 1 }$ 
D)  $f ( x ) = \frac { 2 } { x ^ { 2 } - 1 }$

Question 13

Find the equation that the given graph represents.
-

Accepted Answer

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

Question 14

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 1 } { x + 5 }$$

Accepted Answer

A)  Domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
C)  Domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 5 ) \cup ( 5 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  Domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
C)  Domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 5 ) \cup ( 5 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 15

Find an equation for the rational function graph.
-

Accepted Answer

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

Question 16

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 3 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }$$

Accepted Answer

A)  $- 8$ (multiplicity 2 ), 8 (multiplicity 3 ) 
B)  $- 8$ (multiplicity 3), 8 (multiplicity 2 ) 
C)  4 (multiplicity 1), 8 (multiplicity 1), $- 8$ (multiplicity 1 ) 
D)  4 (multiplicity 1), $- 8$ (multiplicity 3), 8 (multiplicity 3) 
A)  $- 8$ (multiplicity 2 ), 8 (multiplicity 3 ) 
B)  $- 8$ (multiplicity 3), 8 (multiplicity 2 ) 
C)  4 (multiplicity 1), 8 (multiplicity 1), $- 8$ (multiplicity 1 ) 
D)  4 (multiplicity 1), $- 8$ (multiplicity 3), 8 (multiplicity 3)

Question 17

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 2.73 x ^ { 4 } + 3 x ^ { 2 } + x - 2$$

Accepted Answer

A)  
  
B)

C)

D)

A)  
  
B)

C)

D)

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 7 x - 8 > 0$$

Accepted Answer

A)  $( - 8,1 )$ 
B)  $( \infty , - 8 ) \cup ( 1 , \infty )$ 
C)  $( \infty , - 1 ) \cup ( 8 , \infty )$ 
D)  $( - 1,8 )$ 
A)  $( - 8,1 )$ 
B)  $( \infty , - 8 ) \cup ( 1 , \infty )$ 
C)  $( \infty , - 1 ) \cup ( 8 , \infty )$ 
D)  $( - 1,8 )$

Question 19

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = 4 x ^ { 3 } + ( 7 - 4 i ) x ^ { 2 } + ( - 14 - 11 i ) x + 3 + 3 i ; k = 1 + i$$

Accepted Answer

A)  $( x - ( 1 + i ) ) ( x + 3 ) ( 4 x - 1 )$ 
B)  $( x + ( 1 + i ) ) ( x - 3 ) ( 4 x + 1 )$ 
C)  $( x - ( 1 + i ) ) ( x - 3 ) ( 4 x + 1 )$ 
D)  $( x - ( 1 + i ) ) ( x + 2 ) ( 4 x - 1 )$ 
A)  $( x - ( 1 + i ) ) ( x + 3 ) ( 4 x - 1 )$ 
B)  $( x + ( 1 + i ) ) ( x - 3 ) ( 4 x + 1 )$ 
C)  $( x - ( 1 + i ) ) ( x - 3 ) ( 4 x + 1 )$ 
D)  $( x - ( 1 + i ) ) ( x + 2 ) ( 4 x - 1 )$

Question 20

Determine which of the rational functions given below has the following feature(s).
-x-intercepts: $( - 5,0 )$ and $( 2,0 )$, $y$-intercepts: none, vertical asymptotes: $x = 0$ and $x = 1$, horizontal asymptote: $y = 1$

Accepted Answer

A)  $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { x ( x - 1 ) }$ 
B)  $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { ( x - 1 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { x ( x + 1 ) }$ 
D)  $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { ( x + 1 ) }$ 
A)  $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { x ( x - 1 ) }$ 
B)  $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { ( x - 1 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { x ( x + 1 ) }$ 
D)  $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { ( x + 1 ) }$

Use synthetic division to perform the division. - $\frac { x ^ { 3 } + \frac { 5 } { 2 } x ^ { 2 } - 2 x - \frac { 3 } { 2 } } { x + \frac { 1 } { 2 } }$

Solve. -The data in the table show the number of burglaries reported in a small town for several years on record. Year \# of Burglaries 0 8 2 5 4 6 6 3 7 3 8 2 11 2 13 3 15 3 Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Determine which of the rational functions given below has the following feature(s). -The vertical asymptote is x = 5

Provide an appropriate response. -What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

Give all possible rational zeros for the following polynomial. - $P ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 5 } { x - 5 }$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { - 4 } { x ^ { 2 } } \text { is symmetrical with respect to the } y \text {-axis. }$

Graph the function. - $f ( x ) = \frac { 7 } { x ^ { 2 } }$ $Graph the function. - f ( x ) = \frac { 7 } { x ^ { 2 } }$

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

Find an equation for the rational function graph. -

Find the equation that the given graph represents. -

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { x + 5 }$

Find an equation for the rational function graph. -

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 3 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 2.73 x ^ { 4 } + 3 x ^ { 2 } + x - 2$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 7 x - 8 > 0$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 4 x ^ { 3 } + ( 7 - 4 i ) x ^ { 2 } + ( - 14 - 11 i ) x + 3 + 3 i ; k = 1 + i$

Determine which of the rational functions given below has the following feature(s). -x-intercepts: $( - 5,0 )$ and $( 2,0 )$ , $y$ -intercepts: none, vertical asymptotes: $x = 0$ and $x = 1$ , horizontal asymptote: $y = 1$

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

Use synthetic division to perform the division. - x3+52x2−2x−32x+12\frac { x ^ { 3 } + \frac { 5 } { 2 } x ^ { 2 } - 2 x - \frac { 3 } { 2 } } { x + \frac { 1 } { 2 } }x+21​x3+25​x2−2x−23​​

Solve. -The data in the table show the number of burglaries reported in a small town for several years on record. Year \# of Burglaries 0 8 2 5 4 6 6 3 7 3 8 2 11 2 13 3 15 3 Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Determine which of the rational functions given below has the following feature(s). -The vertical asymptote is x = 5

Provide an appropriate response. -What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

Give all possible rational zeros for the following polynomial. - P(x)=13x3+23x2+2x−26P ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26P(x)=13x3+23x2+2x−26

Give the equations of any vertical asymptotes. - h(x)=5x−5h ( x ) = \frac { 5 } { x - 5 }h(x)=x−55​

Graph the function. - f(x)=7x2f ( x ) = \frac { 7 } { x ^ { 2 } }f(x)=x27​

Find the equation of the axis of symmetry of the parabola. - f(x)=x2+2f ( x ) = x ^ { 2 } + 2f(x)=x2+2

Find an equation for the rational function graph. -

Find the equation that the given graph represents. -

Give the domain and range for the rational function. Use interval notation. - f(x)=1x+5f ( x ) = \frac { 1 } { x + 5 }f(x)=x+51​

Find an equation for the rational function graph. -

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=3(x+8)2(x−8)3f ( x ) = 3 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }f(x)=3(x+8)2(x−8)3

Find the correct end behavior diagram for the given polynomial function. - P(x)=2.73x4+3x2+x−2P ( x ) = 2.73 x ^ { 4 } + 3 x ^ { 2 } + x - 2P(x)=2.73x4+3x2+x−2

Solve the inequality. Write the solution set in interval notation. - x2−7x−8>0x ^ { 2 } - 7 x - 8 > 0x2−7x−8>0

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=4x3+(7−4i)x2+(−14−11i)x+3+3i;k=1+if ( x ) = 4 x ^ { 3 } + ( 7 - 4 i ) x ^ { 2 } + ( - 14 - 11 i ) x + 3 + 3 i ; k = 1 + if(x)=4x3+(7−4i)x2+(−14−11i)x+3+3i;k=1+i

Determine which of the rational functions given below has the following feature(s). -x-intercepts: (−5,0)( - 5,0 )(−5,0) and (2,0)( 2,0 )(2,0) , yyy -intercepts: none, vertical asymptotes: x=0x = 0x=0 and x=1x = 1x=1 , horizontal asymptote: y=1y = 1y=1

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

Use synthetic division to perform the division. - $\frac { x ^ { 3 } + \frac { 5 } { 2 } x ^ { 2 } - 2 x - \frac { 3 } { 2 } } { x + \frac { 1 } { 2 } }$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 5 } { x - 5 }$

Graph the function. - $f ( x ) = \frac { 7 } { x ^ { 2 } }$ $Graph the function. - f ( x ) = \frac { 7 } { x ^ { 2 } }$

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

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { x + 5 }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 3 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 2.73 x ^ { 4 } + 3 x ^ { 2 } + x - 2$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 7 x - 8 > 0$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 4 x ^ { 3 } + ( 7 - 4 i ) x ^ { 2 } + ( - 14 - 11 i ) x + 3 + 3 i ; k = 1 + i$

Determine which of the rational functions given below has the following feature(s). -x-intercepts: $( - 5,0 )$ and $( 2,0 )$ , $y$ -intercepts: none, vertical asymptotes: $x = 0$ and $x = 1$ , horizontal asymptote: $y = 1$