Question 1

Graph the function.
-$f(x)=\frac{3}{x+4}$

Accepted Answer

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

Question 2

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f.
-

Accepted Answer

A)  Vertical: $x = - 1$; horizontal: $y = 3 ; ( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  Vertical: $x = 3$; horizontal: $y = - 1 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
C)  Vertical: $x = 3$; horizontal: $y = - 1 ; ( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  Vertical: $x = - 1$; horizontal: $y = 3 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
A)  Vertical: $x = - 1$; horizontal: $y = 3 ; ( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  Vertical: $x = 3$; horizontal: $y = - 1 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
C)  Vertical: $x = 3$; horizontal: $y = - 1 ; ( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  Vertical: $x = - 1$; horizontal: $y = 3 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$

Question 3

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

Accepted Answer

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

Question 4

Solve the problem.
-A plane suddenly experiences turbulence while in flight. At this point the change in its altitude, in feet, is represented by the following function of time: $F ( x ) = \frac { 5 ( x - 10 ) ^ { 2 } - 19 } { 20 ( x - 10 ) ^ { 2 } - 10 ( x - 10 ) + 17 }$.

Assuming that the turbulence first hits at time $x = 0$, what is the maximum relative drop the plane will experience due to turbulence? (Round the result to the nearest hundredth.)

Accepted Answer

A)  $28.39 \mathrm { ft }$ 
B)  $10.21 \mathrm { ft }$ 
C)  $0.25 \mathrm { ft }$ 
D)  $1.19 \mathrm { ft }$ 
A)  $28.39 \mathrm { ft }$ 
B)  $10.21 \mathrm { ft }$ 
C)  $0.25 \mathrm { ft }$ 
D)  $1.19 \mathrm { ft }$

Question 5

Provide an appropriate response.
-How many real zeros does this graph have?

Accepted Answer

A)  1 
B)  4 
C)  2 
D)  3 
A)  1 
B)  4 
C)  2 
D)  3

Question 6

Sketch the graph of the rational function.
-$$f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$$

Accepted Answer

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

Question 7

Solve the problem.
-The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.3 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where $t$ is time in years. After what year does income begin to decline?

Accepted Answer

A)  $5.5 \mathrm { yr }$ 
B)  $6.5 \mathrm { yr }$ 
C)  $13 \mathrm { yr }$ 
D)  $8.67 \mathrm { yr }$ 
A)  $5.5 \mathrm { yr }$ 
B)  $6.5 \mathrm { yr }$ 
C)  $13 \mathrm { yr }$ 
D)  $8.67 \mathrm { yr }$

Question 8

Answer the question
-Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z?

Accepted Answer

A)  $\mathrm { z }$ is one-sixth as large as before 
B)  z is multiplied by $\frac { 1 } { 18 }$ 
C)  $z$ is six times as large as before 
D)  $z$ is multiplied by $\frac { 2 } { 9 }$ 
A)  $\mathrm { z }$ is one-sixth as large as before 
B)  z is multiplied by $\frac { 1 } { 18 }$ 
C)  $z$ is six times as large as before 
D)  $z$ is multiplied by $\frac { 2 } { 9 }$

Question 9

Solve the problem.
-The number of mosquitoes $M ( x )$, in millions, in a certain area depends on the June rainfall $x$, in inches, according to the equation $M ( x ) = 6 x - x ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?

Accepted Answer

A)  3 in. 
B)  $6 \mathrm { in. }$ 
C)  $0 \mathrm { in }$. 
D)  $36 \mathrm { in. }$ 
A)  3 in. 
B)  $6 \mathrm { in. }$ 
C)  $0 \mathrm { in }$. 
D)  $36 \mathrm { in. }$

Question 10

Provide an appropriate response.
-Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 5 } { x - 4 }$

Accepted Answer

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

Question 11

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.
-

Accepted Answer

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

Question 12

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

Accepted Answer

A)  $\mathrm { y } = 2$ 
B)  $y = 0$ 
C)  $x = - 2$ 
D)  $x = 2$ 
A)  $\mathrm { y } = 2$ 
B)  $y = 0$ 
C)  $x = - 2$ 
D)  $x = 2$

Question 13

Give the equation of any oblique asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } - 9 x + 8 } { x + 8 }$$

Accepted Answer

A)  $y = x + 17$ 
B)  none 
C)  $y = x - 17$ 
D)  $x = y + 9$ 
A)  $y = x + 17$ 
B)  none 
C)  $y = x - 17$ 
D)  $x = y + 9$

Question 14

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$$

Accepted Answer

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

Question 15

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $1 , - 2,3$ and $P ( 2 ) = 8$

Accepted Answer

A)  $P ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 10 x + 12$ 
B)  $P ( x ) = - 2 x ^ { 3 } - 8 x ^ { 2 } + 10 x - 12$ 
C)  $P ( x ) = 2 x ^ { 3 } - 4 x ^ { 2 } - 10 x + 12$ 
D)  $P ( x ) = - 2 x ^ { 3 } + 4 x ^ { 2 } + 10 x - 12$ 
A)  $P ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 10 x + 12$ 
B)  $P ( x ) = - 2 x ^ { 3 } - 8 x ^ { 2 } + 10 x - 12$ 
C)  $P ( x ) = 2 x ^ { 3 } - 4 x ^ { 2 } - 10 x + 12$ 
D)  $P ( x ) = - 2 x ^ { 3 } + 4 x ^ { 2 } + 10 x - 12$

Question 16

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$$

Accepted Answer

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

Question 17

Solve the problem.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the
Attraction when the masses are 6 ft apart?

Accepted Answer

A)  4 lb 
B)  3 lb 
C)  2 lb 
D)  1 lb 
A)  4 lb 
B)  3 lb 
C)  2 lb 
D)  1 lb

Question 18

Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$-intercepts?

Accepted Answer

A) $a > 9$ B) $a 3$ D) $a < 3$ A) $a > 9$ B) $a 3$ D) $a < 3$

Question 19

Find the domain and range of the function.
-$$f ( x ) = x ^ { 2 } + 8$$

Accepted Answer

A)  Domain: $( - 8 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( 8 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $[ 8 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $( - 8 , \infty )$ 
A)  Domain: $( - 8 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( 8 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $[ 8 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $( - 8 , \infty )$

Question 20

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f.
-

Accepted Answer

A)  Vertical: $x = - 1$; horizontal: $y = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Vertical: $x = 0$; horizontal: $y = - 1 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Vertical: $x = 0$; horizontal: $y = - 1 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
D)  Vertical: $x = - 1$; horizontal: $y = 0 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
A)  Vertical: $x = - 1$; horizontal: $y = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Vertical: $x = 0$; horizontal: $y = - 1 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Vertical: $x = 0$; horizontal: $y = - 1 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
D)  Vertical: $x = - 1$; horizontal: $y = 0 ; ( - \infty , - 1 ) \cup ( - 1 , \infty )$

Graph the function. - $f(x)=\frac{3}{x+4}$ $Graph the function. - f(x)=\frac{3}{x+4}$

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

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

Provide an appropriate response. -How many real zeros does this graph have?

Sketch the graph of the rational function. - $f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$

Solve the problem. -The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.3 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where $t$ is time in years. After what year does income begin to decline?

Answer the question -Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z?

Solve the problem. -The number of mosquitoes $M ( x )$ , in millions, in a certain area depends on the June rainfall $x$ , in inches, according to the equation $M ( x ) = 6 x - x ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 5 } { x - 4 }$

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. -

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

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } - 9 x + 8 } { x + 8 }$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $1 , - 2,3$ and $P ( 2 ) = 8$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the Attraction when the masses are 6 ft apart?

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } + 8$

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

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

Graph the function. - f(x)=3x+4f(x)=\frac{3}{x+4}f(x)=x+43​

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Graph the function. - f(x)=2−2xf(x)=2-\frac{2}{x}f(x)=2−x2​

Provide an appropriate response. -How many real zeros does this graph have?

Sketch the graph of the rational function. - f(x)=2xx2+4x+3f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }f(x)=x2+4x+32x​

Answer the question -Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z?

Solve the problem. -The number of mosquitoes M(x)M ( x )M(x) , in millions, in a certain area depends on the June rainfall xxx , in inches, according to the equation M(x)=6x−x2M ( x ) = 6 x - x ^ { 2 }M(x)=6x−x2 . What rainfall produces the maximum number of mosquitoes?

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)=5x−4f ( x ) = \frac { 5 } { x - 4 }f(x)=x−45​

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. -

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

Give the equation of any oblique asymptotes. - f(x)=x2−9x+8x+8f ( x ) = \frac { x ^ { 2 } - 9 x + 8 } { x + 8 }f(x)=x+8x2−9x+8​

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3−3x2−5x+39f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39f(x)=x3−3x2−5x+39

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of 1,−2,31 , - 2,31,−2,3 and P(2)=8P ( 2 ) = 8P(2)=8

Sketch the graph of the rational function. - f(x)=x2−4x−2f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }f(x)=x−2x2−4​

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the Attraction when the masses are 6 ft apart?

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2−6x+3f ( x ) = a x ^ { 2 } - 6 x + 3f(x)=ax2−6x+3 have no xxx -intercepts?

Find the domain and range of the function. - f(x)=x2+8f ( x ) = x ^ { 2 } + 8f(x)=x2+8

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

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

Graph the function. - $f(x)=\frac{3}{x+4}$ $Graph the function. - f(x)=\frac{3}{x+4}$

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

Sketch the graph of the rational function. - $f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$

Solve the problem. -The number of mosquitoes $M ( x )$ , in millions, in a certain area depends on the June rainfall $x$ , in inches, according to the equation $M ( x ) = 6 x - x ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 5 } { x - 4 }$

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. -

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

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } - 9 x + 8 } { x + 8 }$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $1 , - 2,3$ and $P ( 2 ) = 8$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } + 8$