Question 1

Find the domain and range of the function.
-$$f ( x ) = x ^ { 2 } + 4$$

Accepted Answer

A)  Domain: $( - 4 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $( - 4 , \infty )$ 
C)  Domain: $( 4 , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 4 , \infty )$ 
A)  Domain: $( - 4 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $( - 4 , \infty )$ 
C)  Domain: $( 4 , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 4 , \infty )$

Question 2

Find the equation that the given graph represents.
-

Accepted Answer

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

Question 3

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = x ^ { 3 } - 12 x - 16 ; k = - 2 \text { (multiplicity 2) }$$

Accepted Answer

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

Question 4

Provide an appropriate response.
-Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 1 } { x - 9 }$

Accepted Answer

A)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
B)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
C)  Approaches $\infty$ from the left and the right 
D)  Approaches $- \infty$ from the left and the right 
A)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
B)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
C)  Approaches $\infty$ from the left and the right 
D)  Approaches $- \infty$ from the left and the right

Question 5

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } + 10 x - 8$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 8 } , \pm 2$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 4 , \pm 8$ 
C)  $\pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm 1 , \pm 2 , \pm 4$ 
A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 8 } , \pm 2$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 4 , \pm 8$ 
C)  $\pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm 1 , \pm 2 , \pm 4$

Question 6

Translate the given formula to an English phrase using the word "varies".
-$\mathrm { P } = \frac { \mathrm { kNT } } { \mathrm { V } }$ , where P is the gas pressure of N molecules of a gas in a volume V at temperature T

Accepted Answer

Pressure varies dire

Question 7

Determine whether the statement is true or false.
-$f(x)=-\frac{6}{x}$

Accepted Answer

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

Question 8

Find the equation of the axis of symmetry of the parabola.
-$$f ( x ) = ( x + 9 ) ^ { 2 } - 2$$

Accepted Answer

A)  $y = 2$ 
B)  $x = 2$ 
C)  $x = 9$ 
D)  $x = - 9$ 
A)  $y = 2$ 
B)  $x = 2$ 
C)  $x = 9$ 
D)  $x = - 9$

Question 9

Give the equations of any vertical asymptotes.
-$$f ( x ) = \frac { x - 4 } { x ^ { 2 } + 5 }$$

Accepted Answer

A)  $x = 2 , x = - 2$ 
B)  $x = 5$ 
C)  $x = - 5$ 
D)  none 
A)  $x = 2 , x = - 2$ 
B)  $x = 5$ 
C)  $x = - 5$ 
D)  none

Question 10

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 6 , i , - i$ and $P ( - 3 ) = 60$

Accepted Answer

A)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } - 2 x - 12$ 
B)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } + 2 x + 12$ 
C)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } + 2 x + 12$ 
D)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } - 2 x - 12$ 
A)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } - 2 x - 12$ 
B)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } + 2 x + 12$ 
C)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } + 2 x + 12$ 
D)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } - 2 x - 12$

Question 11

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

Question 12

The length of a rectangle is 10 inches more than its width. If 5 inches are taken from the length and added to the width, the figure becomes a square with an area of 289 square inches. What are the dimensions of the original
Figure?

Accepted Answer

A)  17 in. by 17 in. 
B)  12 in. by 22 in. 
C)  7 in. by 17 in. 
D)  12 in. by 17 in. 
A)  17 in. by 17 in. 
B)  12 in. by 22 in. 
C)  7 in. by 17 in. 
D)  12 in. by 17 in.

Question 13

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: $M ( x ) = 16 x - x ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

Accepted Answer

A)  16 in. 
B)  256 in. 
C)  0 in. 
D)  8 in. 
A)  16 in. 
B)  256 in. 
C)  0 in. 
D)  8 in.

Question 14

The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled  40,000 mi has  $\frac { 5 } { 8 }$  in. of tread left. How much tread will be left on a tire that has traveled  19,000 mi ?

Accepted Answer

A)  $\frac { 25 } { 19 } \text { in. }$ 
B)  $\frac { 19 } { 25 } \text { in. }$ 
C)   64,000 in. 
D)  $\frac { 1 } { 64000 } \text { in. }$ 
A)  $\frac { 25 } { 19 } \text { in. }$ 
B)  $\frac { 19 } { 25 } \text { in. }$ 
C)   64,000 in. 
D)  $\frac { 1 } { 64000 } \text { in. }$

Question 15

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.
-

Accepted Answer

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

Question 16

The population of a city has varied considerably in recent years. The data in the table relates the population P to time t, in years. Use a quadratic function fitted to the data to predict the population in year 10. $$\begin{array} { c | c } 
\text { Year, t } & \text { Population, P } \
\hline 0 & 59,000 \
\hline 1 & 48,000 \
\hline 2 & 43,500 \
\hline 3 & 49,000 \
\hline 4 & 41,500 \
\hline 5 & 39,000 \
\hline 6 & 42,500
\end{array}$$

Accepted Answer

A)  81,202 
B)  48,431 
C)  119,000 
D)  58,964 
A)  81,202 
B)  48,431 
C)  119,000 
D)  58,964

Question 17

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = x ^ { 3 } + 9 x$ 
B)  $P ( x ) = - x ^ { 3 } + 20 x$ 
C)  $P ( x ) = - x ^ { 3 } + 4 x ^ { 2 } - 9$ 
D)  $P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 20 x$ 
A)  $P ( x ) = x ^ { 3 } + 9 x$ 
B)  $P ( x ) = - x ^ { 3 } + 20 x$ 
C)  $P ( x ) = - x ^ { 3 } + 4 x ^ { 2 } - 9$ 
D)  $P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 20 x$

Question 18

Find the equation that the given graph represents.
-

Accepted Answer

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

Question 19

What is the smallest possible degree of the function for which this graph represents?

Accepted Answer

A)  4 
B)  3 
C)  2 
D)  5 
A)  4 
B)  3 
C)  2 
D)  5

Question 20

Match the equation to the correct graph.
-$$y = ( x + 5 ) ^ { 2 }$$

Accepted Answer

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

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } + 4$

Find the equation that the given graph represents. -

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 12 x - 16 ; k = - 2 \text { (multiplicity 2) }$

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 1 } { x - 9 }$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } + 10 x - 8$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { P } = \frac { \mathrm { kNT } } { \mathrm { V } }$ , where P is the gas pressure of N molecules of a gas in a volume V at temperature T

Determine whether the statement is true or false. - $f(x)=-\frac{6}{x}$ $Determine whether the statement is true or false. - f(x)=-\frac{6}{x}$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 9 ) ^ { 2 } - 2$

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 5 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 6 , i , - i$ and $P ( - 3 ) = 60$

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

The length of a rectangle is 10 inches more than its width. If 5 inches are taken from the length and added to the width, the figure becomes a square with an area of 289 square inches. What are the dimensions of the original Figure?

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: $M ( x ) = 16 x - x ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 40,000 mi has $\frac { 5 } { 8 }$ in. of tread left. How much tread will be left on a tire that has traveled 19,000 mi ?

The population of a city has varied considerably in recent years. The data in the table relates the population P to time t, in years. Use a quadratic function fitted to the data to predict the population in year 10. Year, t Population, P 0 59,000 1 48,000 2 43,500 3 49,000 4 41,500 5 39,000 6 42,500

Find the equation that the given graph represents. -

Find the equation that the given graph represents. -

What is the smallest possible degree of the function for which this graph represents?

Match the equation to the correct graph. - $y = ( x + 5 ) ^ { 2 }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Find the domain and range of the function. - f(x)=x2+4f ( x ) = x ^ { 2 } + 4f(x)=x2+4

Find the equation that the given graph represents. -

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=x3−12x−16;k=−2 (multiplicity 2) f ( x ) = x ^ { 3 } - 12 x - 16 ; k = - 2 \text { (multiplicity 2) }f(x)=x3−12x−16;k=−2 (multiplicity 2)

Provide an appropriate response. -Explain the behavior of the graph of f(x)f ( x )f(x) as it approaches its vertical asymptote. f(x)=1x−9f ( x ) = \frac { 1 } { x - 9 }f(x)=x−91​

Give all possible rational zeros for the following polynomial. - P(x)=2x3+6x2+10x−8P ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } + 10 x - 8P(x)=2x3+6x2+10x−8

Translate the given formula to an English phrase using the word "varies". - P=kNTV\mathrm { P } = \frac { \mathrm { kNT } } { \mathrm { V } }P=VkNT​ , where P is the gas pressure of N molecules of a gas in a volume V at temperature T

Determine whether the statement is true or false. - f(x)=−6xf(x)=-\frac{6}{x}f(x)=−x6​

Find the equation of the axis of symmetry of the parabola. - f(x)=(x+9)2−2f ( x ) = ( x + 9 ) ^ { 2 } - 2f(x)=(x+9)2−2

Give the equations of any vertical asymptotes. - f(x)=x−4x2+5f ( x ) = \frac { x - 4 } { x ^ { 2 } + 5 }f(x)=x2+5x−4​

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −6,i,−i- 6 , i , - i−6,i,−i and P(−3)=60P ( - 3 ) = 60P(−3)=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

The length of a rectangle is 10 inches more than its width. If 5 inches are taken from the length and added to the width, the figure becomes a square with an area of 289 square inches. What are the dimensions of the original Figure?

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x)=16x−x2M ( x ) = 16 x - x ^ { 2 }M(x)=16x−x2 . What rainfall produces the maximum number of mosquitoes?

The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 40,000 mi has 58\frac { 5 } { 8 }85​ in. of tread left. How much tread will be left on a tire that has traveled 19,000 mi ?

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 x2x ^ { 2 }x2 should be positive or negative. -

Find the equation that the given graph represents. -

Find the equation that the given graph represents. -

What is the smallest possible degree of the function for which this graph represents?

Match the equation to the correct graph. - y=(x+5)2y = ( x + 5 ) ^ { 2 }y=(x+5)2

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } + 4$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 12 x - 16 ; k = - 2 \text { (multiplicity 2) }$

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 1 } { x - 9 }$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } + 10 x - 8$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { P } = \frac { \mathrm { kNT } } { \mathrm { V } }$ , where P is the gas pressure of N molecules of a gas in a volume V at temperature T

Determine whether the statement is true or false. - $f(x)=-\frac{6}{x}$ $Determine whether the statement is true or false. - f(x)=-\frac{6}{x}$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 9 ) ^ { 2 } - 2$

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 5 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 6 , i , - i$ and $P ( - 3 ) = 60$

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

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: $M ( x ) = 16 x - x ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 40,000 mi has $\frac { 5 } { 8 }$ in. of tread left. How much tread will be left on a tire that has traveled 19,000 mi ?

Match the equation to the correct graph. - $y = ( x + 5 ) ^ { 2 }$