Question 1

Solve the equation in the real number system.
-$$2 x ^ { 3 } - 13 x ^ { 2 } + 22 x - 8 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } , 2,4 \right\}$ 
B)  $\{ - 2,1 , - 2 \rangle$ 
C)  $\{ 2,1,2 \}$ 
D)  $\left\{ - \frac { 1 } { 2 } , 2 , - 4 \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } , 2,4 \right\}$ 
B)  $\{ - 2,1 , - 2 \rangle$ 
C)  $\{ 2,1,2 \}$ 
D)  $\left\{ - \frac { 1 } { 2 } , 2 , - 4 \right\}$ A

Question 2

Find a bound on the real zeros of the polynomial function.
-f(x) = x4 + 2x2 - 3

Accepted Answer

A)  -5 and 5 
B)  -4 and 4 
C)  -6 and 6 
D)  -3 and 3 
A)  -5 and 5 
B)  -4 and 4 
C)  -6 and 6 
D)  -3 and 3 B

Question 3

f(x) = 3 - (x - 4)4

Accepted Answer

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

Question 4

Accepted Answer

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

Question 5

$$f ( x ) = 4 - ( x + 4 ) ^ { 5 }$$

Accepted Answer

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

Question 6

Determine the maximum number of turning points of f.
-f(x) = -x2 (x + 4)3(x2 - 1)

Accepted Answer

A)  6 
B)  2 
C)  5 
D)  7 
A)  6 
B)  2 
C)  5 
D)  7

Question 7

Solve the equation in the real number system.
-$$2 x ^ { 3 } - x ^ { 2 } - 6 x + 3 = 0$$

Accepted Answer

A)  $\{ 2 , \sqrt { 3 } , - \sqrt { 3 } \}$ 
B)  $\left\{ - \frac { 1 } { 2 } , \sqrt { 3 } , - \sqrt { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , \sqrt { 3 } , - \sqrt { 3 } \right\}$ 
D)  $\{ - 2 , \sqrt { 3 } , - \sqrt { 3 } \}$ 
A)  $\{ 2 , \sqrt { 3 } , - \sqrt { 3 } \}$ 
B)  $\left\{ - \frac { 1 } { 2 } , \sqrt { 3 } , - \sqrt { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , \sqrt { 3 } , - \sqrt { 3 } \right\}$ 
D)  $\{ - 2 , \sqrt { 3 } , - \sqrt { 3 } \}$

Question 8

$f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$

Accepted Answer

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

Question 9

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = 11 x ^ { 3 } - x ^ { 2 } + 3$$

Accepted Answer

A)  $\pm \frac { 1 } { 11 } , \pm \frac { 3 } { 11 } , \pm 1 , \pm 3 , \pm 11$ 
B)  $\pm \frac { 1 } { 11 } , \pm \frac { 3 } { 11 } , \pm 1 , \pm 3$ 
C)  $\pm \frac { 1 } { 11 } , \pm \frac { 1 } { 3 } , \pm 1 , \pm 3 , \pm 11$ 
D)  $\pm \frac { 1 } { 3 } , \pm \frac { 11 } { 3 } , \pm 1 , \pm 11$ 
A)  $\pm \frac { 1 } { 11 } , \pm \frac { 3 } { 11 } , \pm 1 , \pm 3 , \pm 11$ 
B)  $\pm \frac { 1 } { 11 } , \pm \frac { 3 } { 11 } , \pm 1 , \pm 3$ 
C)  $\pm \frac { 1 } { 11 } , \pm \frac { 1 } { 3 } , \pm 1 , \pm 3 , \pm 11$ 
D)  $\pm \frac { 1 } { 3 } , \pm \frac { 11 } { 3 } , \pm 1 , \pm 11$

Question 10

Solve the problem.
-For the polynomial funct $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$
 a) Find the x- and y-intercepts of the graph of f. Round to two decimal places, if necessary.
b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
c) End behavior: find the power function that the graph of f resembles for large values of |x|.
d) Use a graphing utility to graph the function.Approximate the local maxima rounded to two decimal places,
if necessary. Approximate the local minima rounded to two decimal places, if necessary.
e) Determine the number of turning points on the graph.
f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the
graph of f.

Accepted Answer

a) The @#LAT-DLM&-intercepts are @#LAT-DLM&, and @#LAT-DLM&. The @#LAT-DLM&-inte

Question 11

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = x ^ { 5 } - 5 x ^ { 2 } + 2 x + 7$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 7 }$ 
B)  $\pm 7 , \pm \frac { 1 } { 7 }$ 
C)  $\pm \frac { 1 } { 5 } , \pm \frac { 7 } { 5 } , \pm 7$ 
D)  $\pm 1 , \pm 7$ 
A)  $\pm 1 , \pm \frac { 1 } { 7 }$ 
B)  $\pm 7 , \pm \frac { 1 } { 7 }$ 
C)  $\pm \frac { 1 } { 5 } , \pm \frac { 7 } { 5 } , \pm 7$ 
D)  $\pm 1 , \pm 7$

Question 12

Solve the equation in the real number system.
-$$x ^ { 4 } - 12 x ^ { 2 } - 64 = 0$$

Accepted Answer

A)  {-8, 8} 
B)  {-4, 4} 
C)  {-2, 2} 
D)  {-4, -2, 2, 4} 
A)  {-8, 8} 
B)  {-4, 4} 
C)  {-2, 2} 
D)  {-4, -2, 2, 4}

Question 13

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-f(x) = 9x3 + 7x2 - 9x - 9; [1, 2]

Accepted Answer

A)  f(1) = -2 and f(2) = -73; no 
B)  f(1) = -2 and f(2) = 73; yes 
C)  f(1) = 2 and f(2) = -73; yes 
D)  f(1) = 2 and f(2) = 73; no 
A)  f(1) = -2 and f(2) = -73; no 
B)  f(1) = -2 and f(2) = 73; yes 
C)  f(1) = 2 and f(2) = -73; yes 
D)  f(1) = 2 and f(2) = 73; no

Question 14

f(x) = x5 + 4

Accepted Answer

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

Question 15

f(x)=5x5

Accepted Answer

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

Question 16

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; \text { zero: } - 4$$

Accepted Answer

A)  $6 + 4 i , 6 - 4 i$ 
B)  $1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
C)  $3 + 2 \mathrm { i } , 3 - 2 \mathrm { i }$ 
D)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$ 
A)  $6 + 4 i , 6 - 4 i$ 
B)  $1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
C)  $3 + 2 \mathrm { i } , 3 - 2 \mathrm { i }$ 
D)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$

Question 17

$$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } \left( x ^ { 2 } - 5 \right) ( x - 3 )$$

Accepted Answer

A)  0 , multiplicity 2 , touches $x$-axis;
3 , multiplicity 1 , crosses $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis 
B)  0 , multiplicity 2 , crosses $x$-axis;
 3 , multiplicity 1 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis; 
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis 
C)  0 , multiplicity 2, crosses x-axis;
 3 , multiplicity 1 , touches $x$-axis 
D)  0 , multiplicity 2 , touches $x$-axis; 
3 , multiplicity 1 , crosses $x$-axis 
A)  0 , multiplicity 2 , touches $x$-axis;
3 , multiplicity 1 , crosses $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis 
B)  0 , multiplicity 2 , crosses $x$-axis;
 3 , multiplicity 1 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis; 
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis 
C)  0 , multiplicity 2, crosses x-axis;
 3 , multiplicity 1 , touches $x$-axis 
D)  0 , multiplicity 2 , touches $x$-axis; 
3 , multiplicity 1 , crosses $x$-axis

Question 18

f(x) = (x - 3)4 + 4

Accepted Answer

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

Question 19

$$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 5 \right)$$

Accepted Answer

A)  0 , multiplicity 4 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis 
B)  0 , multiplicity 4 , crosses $x$-axis 
C)  0 , multiplicity 4 , crosses $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis; 
D)  0 , multiplicity 4 , touches $x$-axis
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis 
A)  0 , multiplicity 4 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis 
B)  0 , multiplicity 4 , crosses $x$-axis 
C)  0 , multiplicity 4 , crosses $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis; 
D)  0 , multiplicity 4 , touches $x$-axis
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis

Question 20

Find the x- and y-intercepts of f.
-$$f ( x ) = 6 x - x ^ { 3 }$$

Accepted Answer

A)  x-intercepts: $0 , \sqrt { 6 } , - \sqrt { 6 } ; y$-intercept: 0 
B)  x-intercepts: $0 , - 6 ; y$-intercept: 0 
C)  x-intercepts: $0 , - 6 ; y$-intercept: 6 
D)  $x$-intercepts: $0 , \sqrt { 6 } , - \sqrt { 6 } ; y$-intercept: 6 
A)  x-intercepts: $0 , \sqrt { 6 } , - \sqrt { 6 } ; y$-intercept: 0 
B)  x-intercepts: $0 , - 6 ; y$-intercept: 0 
C)  x-intercepts: $0 , - 6 ; y$-intercept: 6 
D)  $x$-intercepts: $0 , \sqrt { 6 } , - \sqrt { 6 } ; y$-intercept: 6

Solve the equation in the real number system. - $2 x ^ { 3 } - 13 x ^ { 2 } + 22 x - 8 = 0$

Find a bound on the real zeros of the polynomial function. -f(x) = x⁴ + 2x² - 3

f(x) = 3 - (x - 4)⁴

$f ( x ) = 4 - ( x + 4 ) ^ { 5 }$ $f ( x ) = 4 - ( x + 4 ) ^ { 5 }$

Determine the maximum number of turning points of f. -f(x) = -x² (x + 4)3(x² - 1)

Solve the equation in the real number system. - $2 x ^ { 3 } - x ^ { 2 } - 6 x + 3 = 0$

$f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$ $f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 11 x ^ { 3 } - x ^ { 2 } + 3$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 5 x ^ { 2 } + 2 x + 7$

Solve the equation in the real number system. - $x ^ { 4 } - 12 x ^ { 2 } - 64 = 0$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = 9x³ + 7x² - 9x - 9; [1, 2]

f(x) = x⁵ + 4

f(x)=5x⁵

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; \text { zero: } - 4$

$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } \left( x ^ { 2 } - 5 \right) ( x - 3 )$

f(x) = (x - 3)4 + 4

$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 5 \right)$

Find the x- and y-intercepts of f. - $f ( x ) = 6 x - x ^ { 3 }$

Functions and Their Graphs

Linear and Quadratic Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 3: Polynomial and Rational Functions

Solve the equation in the real number system. - 2x3−13x2+22x−8=02 x ^ { 3 } - 13 x ^ { 2 } + 22 x - 8 = 02x3−13x2+22x−8=0

Find a bound on the real zeros of the polynomial function. -f(x) = x4 + 2x2 - 3

f(x) = 3 - (x - 4)4

f(x)=4−(x+4)5f ( x ) = 4 - ( x + 4 ) ^ { 5 }f(x)=4−(x+4)5

Determine the maximum number of turning points of f. -f(x) = -x2 (x + 4)3(x2 - 1)

Solve the equation in the real number system. - 2x3−x2−6x+3=02 x ^ { 3 } - x ^ { 2 } - 6 x + 3 = 02x3−x2−6x+3=0

f(x)=12(x−3)5+2f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2f(x)=21​(x−3)5+2

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=11x3−x2+3f ( x ) = 11 x ^ { 3 } - x ^ { 2 } + 3f(x)=11x3−x2+3

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=x5−5x2+2x+7f ( x ) = x ^ { 5 } - 5 x ^ { 2 } + 2 x + 7f(x)=x5−5x2+2x+7

Solve the equation in the real number system. - x4−12x2−64=0x ^ { 4 } - 12 x ^ { 2 } - 64 = 0x4−12x2−64=0

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = 9x3 + 7x2 - 9x - 9; [1, 2]

f(x) = x5 + 4

f(x)=5x5

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=x3−2x2−11x+52; zero: −4f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; \text { zero: } - 4f(x)=x3−2x2−11x+52; zero: −4

f(x)=13x2(x2−5)(x−3)f ( x ) = \frac { 1 } { 3 } x ^ { 2 } \left( x ^ { 2 } - 5 \right) ( x - 3 )f(x)=31​x2(x2−5)(x−3)

f(x) = (x - 3)4 + 4

f(x)=15x4(x2−5)f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 5 \right)f(x)=51​x4(x2−5)

Find the x- and y-intercepts of f. - f(x)=6x−x3f ( x ) = 6 x - x ^ { 3 }f(x)=6x−x3

Functions and Their Graphs

Linear and Quadratic Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Solve the equation in the real number system. - $2 x ^ { 3 } - 13 x ^ { 2 } + 22 x - 8 = 0$

Find a bound on the real zeros of the polynomial function. -f(x) = x⁴ + 2x² - 3

f(x) = 3 - (x - 4)⁴

$f ( x ) = 4 - ( x + 4 ) ^ { 5 }$ $f ( x ) = 4 - ( x + 4 ) ^ { 5 }$

Determine the maximum number of turning points of f. -f(x) = -x² (x + 4)3(x² - 1)

Solve the equation in the real number system. - $2 x ^ { 3 } - x ^ { 2 } - 6 x + 3 = 0$

$f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$ $f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 11 x ^ { 3 } - x ^ { 2 } + 3$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 5 x ^ { 2 } + 2 x + 7$

Solve the equation in the real number system. - $x ^ { 4 } - 12 x ^ { 2 } - 64 = 0$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = 9x³ + 7x² - 9x - 9; [1, 2]

f(x) = x⁵ + 4

f(x)=5x⁵

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; \text { zero: } - 4$

$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } \left( x ^ { 2 } - 5 \right) ( x - 3 )$

$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 5 \right)$

Find the x- and y-intercepts of f. - $f ( x ) = 6 x - x ^ { 3 }$