Question 1

Find the domain and range of the function.
-$$f ( x ) = 1 - x ^ { 2 }$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 1 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 1 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 1 ]$ 
D)  Domain: $( - \infty , 1 ]$; Range: $[ - 1 , \infty )$ 
A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 1 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 1 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 1 ]$ 
D)  Domain: $( - \infty , 1 ]$; Range: $[ - 1 , \infty )$

Question 2

Answer the question
-How can the graph of $f ( x ) = - \frac { 1 } { x } - 10$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Accepted Answer

A)  By reflecting across the $x$-axis and making a vertical shift of 10 units down 
B)  By reflecting across the $y$-axis and making a horizontal shift of 10 units to the left 
C)  By making a horizontal shift of 10 units to the left and a vertical shift of 1 unit down 
D)  By making a horizontal shift of 1 unit to the right and a vertical shift of 10 units up 
A)  By reflecting across the $x$-axis and making a vertical shift of 10 units down 
B)  By reflecting across the $y$-axis and making a horizontal shift of 10 units to the left 
C)  By making a horizontal shift of 10 units to the left and a vertical shift of 1 unit down 
D)  By making a horizontal shift of 1 unit to the right and a vertical shift of 10 units up

Question 3

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$2 - \mathrm { i } , - 6$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 20 x + 30$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x - 30$ 
C)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 19 x + 30$ 
D)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x + 24$ 
A)  $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 20 x + 30$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x - 30$ 
C)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 19 x + 30$ 
D)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x + 24$

Question 4

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) $a > \frac { 16 } { 5 }$ C) $a < \frac { 4 } { 5 }$ D) $a < \frac { 16 } { 5 }$ A) $a > \frac { 4 } { 5 }$ B) $a > \frac { 16 } { 5 }$ C) $a < \frac { 4 } { 5 }$ D) $a < \frac { 16 } { 5 }$

Question 5

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$2 + i ; f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 6

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; - 2 i$$

Accepted Answer

A)  $2 \mathrm { i } , 14 , - 14$ 
B)  $2 \mathrm { i } , 7 , - 7$ 
C)  $2 \mathrm { i } , 7 \mathrm { i } , - 7 \mathrm { i }$ 
D)  $2 \mathrm { i } , 14 \mathrm { i } , - 14 \mathrm { i }$ 
A)  $2 \mathrm { i } , 14 , - 14$ 
B)  $2 \mathrm { i } , 7 , - 7$ 
C)  $2 \mathrm { i } , 7 \mathrm { i } , - 7 \mathrm { i }$ 
D)  $2 \mathrm { i } , 14 \mathrm { i } , - 14 \mathrm { i }$

Question 7

Use the remainder theorem and synthetic division to find f(k).
-$$k = - 3 ; f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 3$$

Accepted Answer

A)  $- 6$ 
B)  48 
C)  $- 48$ 
D)  $- 51$ 
A)  $- 6$ 
B)  48 
C)  $- 48$ 
D)  $- 51$

Question 8

Sketch the graph of the parabola.
-$y=-x^{2}+2 x-8$

Accepted Answer

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

Question 9

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function.
-$$- 3 x ^ { 4 } - 2 x ^ { 3 } - 6 x ^ { 2 } - 4 x + 2 = 0$$

Accepted Answer

A)  Positive $( 2,0 )$, negative $( 2,0 )$ 
B)  Positive (1), negative (1) 
C)  Positive (1), negative $( 3,1 )$ 
D)  Positive (1), negative (2) 
A)  Positive $( 2,0 )$, negative $( 2,0 )$ 
B)  Positive (1), negative (1) 
C)  Positive (1), negative $( 3,1 )$ 
D)  Positive (1), negative (2)

Question 10

Give the equatiosn of any horizontal asymptotes.
-$$f ( x ) = \frac { 7 x ^ { 2 } + 9 } { 7 x ^ { 2 } - 9 }$$

Accepted Answer

A)  $y = 9$ 
B)  $y = 1$ 
C)  $y = - 9$ 
D)  none 
A)  $y = 9$ 
B)  $y = 1$ 
C)  $y = - 9$ 
D)  none

Question 11

Solve the problem.
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting $3 \mathrm {~cm}$ squares from each corner and folding up the sides. Let $x$ represent the width of the original piece of cardboard. Determine a function $\mathrm { V }$ that represents the volume of the box in terms of $x$.

Accepted Answer

A)  $V ( x ) = 6 x ^ { 2 }$ 
B)  $V ( x ) = 3 x ^ { 2 } - 36 x + 108$ 
C)  $V ( x ) = 6 x ^ { 2 } - 27 x + 27$ 
D)  $V ( x ) = 6 x ^ { 2 } - 54 x + 108$ 
A)  $V ( x ) = 6 x ^ { 2 }$ 
B)  $V ( x ) = 3 x ^ { 2 } - 36 x + 108$ 
C)  $V ( x ) = 6 x ^ { 2 } - 27 x + 27$ 
D)  $V ( x ) = 6 x ^ { 2 } - 54 x + 108$

Question 12

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

Accepted Answer

A)  $x = 3 , x = - 3$ 
B)  $x = - 9$ 
C)  $x = 9$ 
D)  none 
A)  $x = 3 , x = - 3$ 
B)  $x = - 9$ 
C)  $x = 9$ 
D)  none

Question 13

Use synthetic division to perform the division.
-$$\frac { x ^ { 5 } + 7 x ^ { 4 } + 7 x ^ { 3 } - 13 x ^ { 2 } + 12 x + 13 } { x + 5 }$$

Accepted Answer

A)  $x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 2 x - 2 + \frac { 5 } { x + 5 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } - 3 x + 2 + \frac { 3 } { x + 5 }$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2 + \frac { 3 } { x + 5 }$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 2 x + 3$ 
A)  $x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 2 x - 2 + \frac { 5 } { x + 5 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } - 3 x + 2 + \frac { 3 } { x + 5 }$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2 + \frac { 3 } { x + 5 }$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 2 x + 3$

Question 14

Solve the problem.
-The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 882 ohms. What is the current when the resistance is
356 ohms? Round to the nearest tenth.

Accepted Answer

A)  0.3 amperes 
B)  0.1 amperes 
C)  19.8 amperes 
D)  3.2 amperes 
A)  0.3 amperes 
B)  0.1 amperes 
C)  19.8 amperes 
D)  3.2 amperes

Question 15

Find the domain and range of the function.
-$$f ( x ) = - x ^ { 2 } - 8 x - 21$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 4 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 5 ]$ 
C)  Domain: $( - \infty , - 5 ]$; Range: $[ 4 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ 5 , \infty )$ 
A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 4 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 5 ]$ 
C)  Domain: $( - \infty , - 5 ]$; Range: $[ 4 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ 5 , \infty )$

Question 16

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 10 x ^ { 3 } + 40 x ^ { 2 } + 2 x - 5$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 5 , \pm \frac { 2 } { 5 } , \pm \frac { 1 } { 10 }$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 5 , \pm \frac { 5 } { 2 } , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 10 }$ 
C)  $\pm 1 , \pm 5 , \pm \frac { 1 } { 2 }$ 
D)  $\pm 1 , \pm \frac { 1 } { 5 } , \pm 2 , \pm \frac { 2 } { 5 } , \pm 5 , \pm 10$ 
A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 5 , \pm \frac { 2 } { 5 } , \pm \frac { 1 } { 10 }$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 5 , \pm \frac { 5 } { 2 } , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 10 }$ 
C)  $\pm 1 , \pm 5 , \pm \frac { 1 } { 2 }$ 
D)  $\pm 1 , \pm \frac { 1 } { 5 } , \pm 2 , \pm \frac { 2 } { 5 } , \pm 5 , \pm 10$

Question 17

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

Accepted Answer

A)  $2 x ^ { 2 } - 3 x - 4 + \frac { - 6 } { x + 2 }$ 
B)  $2 x ^ { 2 } - 3 x - 4$ 
C)  $2 x ^ { 2 } - 3 x + 4 + \frac { - 6 } { x + 2 }$ 
D)  $2 x ^ { 2 } - 3 x + 4$ 
A)  $2 x ^ { 2 } - 3 x - 4 + \frac { - 6 } { x + 2 }$ 
B)  $2 x ^ { 2 } - 3 x - 4$ 
C)  $2 x ^ { 2 } - 3 x + 4 + \frac { - 6 } { x + 2 }$ 
D)  $2 x ^ { 2 } - 3 x + 4$

Question 18

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 36$$

Accepted Answer

A)  $\sqrt { 6 } , - \sqrt { 6 }$ 
B)  $\sqrt { 6 } , - \sqrt { 6 } i , \sqrt { 6 } i , - \sqrt { 6 }$ 
C)  $\sqrt { 6 } , \sqrt { 6 } i$ 
D)  $\sqrt { 6 } , - 6 i , 6 i , - \sqrt { 6 }$ 
A)  $\sqrt { 6 } , - \sqrt { 6 }$ 
B)  $\sqrt { 6 } , - \sqrt { 6 } i , \sqrt { 6 } i , - \sqrt { 6 }$ 
C)  $\sqrt { 6 } , \sqrt { 6 } i$ 
D)  $\sqrt { 6 } , - 6 i , 6 i , - \sqrt { 6 }$

Question 19

Answer the question
-How can the graph of $f ( x ) = \frac { 7 } { x + 11 }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Accepted Answer

A)  By making a horizontal shift of 11 units to the right and stretching vertically by a factor of 7 
B)  By making a horizontal shift of 7 units to the right and a vertical shift of 11 units down 
C)  By making a horizontal shift of 11 units to the left and stretching vertically by a factor of 7 
D)  By making a horizontal shift of 11 units to the left and a vertical shift of 7 units up 
A)  By making a horizontal shift of 11 units to the right and stretching vertically by a factor of 7 
B)  By making a horizontal shift of 7 units to the right and a vertical shift of 11 units down 
C)  By making a horizontal shift of 11 units to the left and stretching vertically by a factor of 7 
D)  By making a horizontal shift of 11 units to the left and a vertical shift of 7 units up

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: $x = 2 ;$ oblique: $y = x - 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$ 
B)  Vertical: $x = - 2$; oblique: $y = x + 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
C)  Vertical: $x = - 2 ;$ oblique; $y = x - 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  Vertical: $x = - 2 ;$ oblique: $\mathrm { y } = \mathrm { x } + 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$ 
A)  Vertical: $x = 2 ;$ oblique: $y = x - 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$ 
B)  Vertical: $x = - 2$; oblique: $y = x + 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
C)  Vertical: $x = - 2 ;$ oblique; $y = x - 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  Vertical: $x = - 2 ;$ oblique: $\mathrm { y } = \mathrm { x } + 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$

Find the domain and range of the function. - $f ( x ) = 1 - x ^ { 2 }$

Answer the question -How can the graph of $f ( x ) = - \frac { 1 } { x } - 10$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $2 - \mathrm { i } , - 6$

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?

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $2 + i ; f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; - 2 i$

Use the remainder theorem and synthetic division to find f(k). - $k = - 3 ; f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 3$

Sketch the graph of the parabola. - $y=-x^{2}+2 x-8$ $Sketch the graph of the parabola. - y=-x^{2}+2 x-8$

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $- 3 x ^ { 4 } - 2 x ^ { 3 } - 6 x ^ { 2 } - 4 x + 2 = 0$

Give the equatiosn of any horizontal asymptotes. - $f ( x ) = \frac { 7 x ^ { 2 } + 9 } { 7 x ^ { 2 } - 9 }$

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

Use synthetic division to perform the division. - $\frac { x ^ { 5 } + 7 x ^ { 4 } + 7 x ^ { 3 } - 13 x ^ { 2 } + 12 x + 13 } { x + 5 }$

Solve the problem. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 882 ohms. What is the current when the resistance is 356 ohms? Round to the nearest tenth.

Find the domain and range of the function. - $f ( x ) = - x ^ { 2 } - 8 x - 21$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 10 x ^ { 3 } + 40 x ^ { 2 } + 2 x - 5$

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

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 36$

Answer the question -How can the graph of $f ( x ) = \frac { 7 } { x + 11 }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

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

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Exam 3: Polynomial and Rational Functions

Find the domain and range of the function. - f(x)=1−x2f ( x ) = 1 - x ^ { 2 }f(x)=1−x2

Answer the question -How can the graph of f(x)=−1x−10f ( x ) = - \frac { 1 } { x } - 10f(x)=−x1​−10 be obtained from the graph of y=1xy = \frac { 1 } { x }y=x1​ ?

Find a polynomial of least degree with only real coefficients and having the given zeros. - 2−i,−62 - \mathrm { i } , - 62−i,−6

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?

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - 2+i;f(x)=x3+2x2−6x+82 + i ; f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 82+i;f(x)=x3+2x2−6x+8

For the polynomial, one zero is given. Find all others. - P(x)=x4−45x2−196;−2iP ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; - 2 iP(x)=x4−45x2−196;−2i

Use the remainder theorem and synthetic division to find f(k). - k=−3;f(x)=−x3+2x2+3k = - 3 ; f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 3k=−3;f(x)=−x3+2x2+3

Sketch the graph of the parabola. - y=−x2+2x−8y=-x^{2}+2 x-8y=−x2+2x−8

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - −3x4−2x3−6x2−4x+2=0- 3 x ^ { 4 } - 2 x ^ { 3 } - 6 x ^ { 2 } - 4 x + 2 = 0−3x4−2x3−6x2−4x+2=0

Give the equatiosn of any horizontal asymptotes. - f(x)=7x2+97x2−9f ( x ) = \frac { 7 x ^ { 2 } + 9 } { 7 x ^ { 2 } - 9 }f(x)=7x2−97x2+9​

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

Use synthetic division to perform the division. - x5+7x4+7x3−13x2+12x+13x+5\frac { x ^ { 5 } + 7 x ^ { 4 } + 7 x ^ { 3 } - 13 x ^ { 2 } + 12 x + 13 } { x + 5 }x+5x5+7x4+7x3−13x2+12x+13​