Question 1

Describe the end behavior of the polynomial function by finding  
-$$f ( x ) = ( x - 3 ) ( 1 - x ) ( 3 x - 5 )$$

Accepted Answer

A)  $\infty , \infty$ 
B)  $- \infty , \infty$ 
C)  $- \infty , - \infty$ 
D)  $\infty , - \infty$ 
A)  $\infty , \infty$ 
B)  $- \infty , \infty$ 
C)  $- \infty , - \infty$ 
D)  $\infty , - \infty$

Question 2

Find the axis of the graph of the function.
-$$f ( x ) = 4 x ^ { 2 } - 8 x + 9$$

Accepted Answer

A)  $x = - 4$ 
B)  $x = 1$ 
C)  $x = 0$ 
D)  $x = 5$ 
A)  $x = - 4$ 
B)  $x = 1$ 
C)  $x = 0$ 
D)  $x = 5$

Question 3

Graph the function.
-$P(x)=(-2 x-1)(x+1)^{2}$

Accepted Answer

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

Question 4

Solve the problem.
-The first column shows the independent variable $( \mathrm { x } )$. The second column shows the dependent variable (y).

Use linear regression to predict the value of $y$ when $x = 43$.

Accepted Answer

A)  $46.16$ 
B)  $63.36$ 
C)  $14.92$ 
D)  $54.76$ 
A)  $46.16$ 
B)  $63.36$ 
C)  $14.92$ 
D)  $54.76$

Question 5

Describe the end behavior of the polynomial function by finding  
-$$f ( x ) = - 6 x ^ { 4 } + 5 x ^ { 2 } - 7$$

Accepted Answer

A)  $-\infty , \infty$ 
B)  $\infty , \infty$ 
C) $\infty , -\infty$ 
D)  $-\infty , -\infty$ 
A)  $-\infty , \infty$ 
B)  $\infty , \infty$ 
C) $\infty , -\infty$ 
D)  $-\infty , -\infty$

Question 6

Write a linear factorization of the function.
-$$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 x + 36$$

Accepted Answer

A)  $f ( x ) = ( x + 4 i ) ( x + 3 i ) ( x - 3 i )$ 
B)  $f ( x ) = ( x + 3 ) ( x + 4 i ) ( x - 4 i )$ 
C)  $f ( x ) = ( x + 4 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( x + 3 i ) ( x + 4 i ) ( x - 4 i )$ 
A)  $f ( x ) = ( x + 4 i ) ( x + 3 i ) ( x - 3 i )$ 
B)  $f ( x ) = ( x + 3 ) ( x + 4 i ) ( x - 4 i )$ 
C)  $f ( x ) = ( x + 4 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( x + 3 i ) ( x + 4 i ) ( x - 4 i )$

Question 7

Solve the problem. Round as appropriate.
-The shadow cast by an object on a sunny day varies directly as the height of the object. If a person 76 inches tall casts a shadow 62 inches long, how tall is a tree which casts a shadow 31 feet in length?

Accepted Answer

A)  69 feet 
B)  38 feet 
C)  152 feet 
D)  25.29 feet 
A)  69 feet 
B)  38 feet 
C)  152 feet 
D)  25.29 feet

Question 8

Solve the polynomial inequality.
-$2 x ^ { 3 } + 9 x ^ { 2 } - 38 x - 21 > 0$

Accepted Answer

A)  $[ - 7 , - 1 / 2 ] \cup [ 3 , \infty )$ 
B)  $( - 7 , - 1 / 2 ) \cup ( 3 , \infty )$ 
C)  $( \infty , - 7 ] \cup [ - 1 / 2,3 ]$ 
D)  $( \infty , - 7 ) \cup ( - 1 / 2,3 )$ 
A)  $[ - 7 , - 1 / 2 ] \cup [ 3 , \infty )$ 
B)  $( - 7 , - 1 / 2 ) \cup ( 3 , \infty )$ 
C)  $( \infty , - 7 ] \cup [ - 1 / 2,3 ]$ 
D)  $( \infty , - 7 ) \cup ( - 1 / 2,3 )$

Question 9

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of
the function f.
-$k = 2 ; f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 2 x + 5$; Lower bound?

Accepted Answer

A) True 
 B)False

Question 10

Solve the problem.
-The profit made when $t$ units are sold, $t > 0$, is given by $P = t ^ { 2 } - 31 t + 228$. Determine the number of units to be sold in order for $\mathrm { P } = 0$ (the break- even point).

Accepted Answer

A)  $t = 31$ 
B)  $\mathrm { t } = 19$ or $\mathrm { t } = 12$ 
C)  $t > 19$ 
D)  $t = - 19$ or $t = - 12$ 
A)  $t = 31$ 
B)  $\mathrm { t } = 19$ or $\mathrm { t } = 12$ 
C)  $t > 19$ 
D)  $t = - 19$ or $t = - 12$

Question 11

The polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$ measures the concentration of a dye in the bloodstream $x$ seconds after it is injected. Does the concentration increase between 10 and 11 seconds?

Accepted Answer

A) True 
 B)False

Question 12

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
-$$x - 4 ; 2 x ^ { 2 } - 14 x + 24$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 13

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) =
1/x.
-$$f ( x ) = \frac { 6 x - 4 } { x - 3 }$$

Accepted Answer

A)  Shift the graph of the reciprocal function right 3 units, stretch vertically by a factor of 14 , and then shift 6 units down. 
B)  Shift the graph of the reciprocal function right 3 units, stretch vertically by a factor of 14 , and then shift 6 units up. 
C)  Shift the graph of the reciprocal function right 3 units, reflect across the x-axis, stretch vertically by a factor of 14 , and then shift 6 units up. 
D)  Shift the graph of the reciprocal function right 3 units, reflect across the x-axis, stretch vertically by a factor of 14, and then shift 6 units down. 
A)  Shift the graph of the reciprocal function right 3 units, stretch vertically by a factor of 14 , and then shift 6 units down. 
B)  Shift the graph of the reciprocal function right 3 units, stretch vertically by a factor of 14 , and then shift 6 units up. 
C)  Shift the graph of the reciprocal function right 3 units, reflect across the x-axis, stretch vertically by a factor of 14 , and then shift 6 units up. 
D)  Shift the graph of the reciprocal function right 3 units, reflect across the x-axis, stretch vertically by a factor of 14, and then shift 6 units down.

Question 14

Find the remainder when f(x) is divided by (x - k)
-$$f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 8 x + 11 ; k = - 2$$

Accepted Answer

A)  3 
B)  $- 29$ 
C)  10 
D)  $- 3$ 
A)  3 
B)  $- 29$ 
C)  10 
D)  $- 3$

Question 15

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative.
-$$f ( x ) = \frac { ( 2 x + 1 ) \sqrt { x - 2 } } { ( x - 8 ) ^ { 2 } }$$

Accepted Answer

A)  (a) $\{ 2 , - 1 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $( 2,8 ) \cup ( 8 , \infty )$, (d) $\varnothing$ 
B)  (a) $\{ 2 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $\varnothing$, (d) $( 2,8 ) \cup ( 8 , \infty )$ 
C)  (a) $\{ 2 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $( 2,8 ) \cup ( 8 , \infty )$, (d) $\varnothing$ 
D)  (a) $\{ 2 , - 1 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $( 2,8 )$, (d) $( 8 , \infty )$ 
A)  (a) $\{ 2 , - 1 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $( 2,8 ) \cup ( 8 , \infty )$, (d) $\varnothing$ 
B)  (a) $\{ 2 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $\varnothing$, (d) $( 2,8 ) \cup ( 8 , \infty )$ 
C)  (a) $\{ 2 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $( 2,8 ) \cup ( 8 , \infty )$, (d) $\varnothing$ 
D)  (a) $\{ 2 , - 1 \}$, (b) $\{ 8 \} \cup ( \infty , 2 )$, (c) $( 2,8 )$, (d) $( 8 , \infty )$

Question 16

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question.
-

Accepted Answer

A)  $f ( x ) = 2 x ^ { 4 } + x ^ { 3 } - 3 x ^ { 2 } - 6 x$ 
B)  $f ( x ) = 2 x ^ { 5 } + x ^ { 3 } + 8 x ^ { 2 } - 4 x + 3$ 
C)  $f ( x ) = - x ^ { 4 } + x ^ { 3 } - x$ 
D)  $f ( x ) = - 3 x ^ { 5 } + x ^ { 4 } + 2 x$ 
A)  $f ( x ) = 2 x ^ { 4 } + x ^ { 3 } - 3 x ^ { 2 } - 6 x$ 
B)  $f ( x ) = 2 x ^ { 5 } + x ^ { 3 } + 8 x ^ { 2 } - 4 x + 3$ 
C)  $f ( x ) = - x ^ { 4 } + x ^ { 3 } - x$ 
D)  $f ( x ) = - 3 x ^ { 5 } + x ^ { 4 } + 2 x$

Question 17

Evaluate the limit based on the graph of f shown.
- 
$\lim _ { x \rightarrow } f ( x )$

Accepted Answer

A)  $\infty$ 
B)  1 
C)  0 
D)  $-\infty$ 
A)  $\infty$ 
B)  1 
C)  0 
D)  $-\infty$

Question 18

Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 11$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 11$ 
B)  $\pm 1 , \pm \frac { 1 } { 11 } , \pm 2 , \pm \frac { 2 } { 11 }$ 
C)  $\pm 1 , \pm 2 , \pm 11 , \pm \frac { 11 } { 2 }$ 
D)  $\pm 1 , \pm 11 , \pm \frac { 1 } { 2 } , \pm \frac { 11 } { 2 }$ 
A)  $\pm 1 , \pm 2 , \pm 11$ 
B)  $\pm 1 , \pm \frac { 1 } { 11 } , \pm 2 , \pm \frac { 2 } { 11 }$ 
C)  $\pm 1 , \pm 2 , \pm 11 , \pm \frac { 11 } { 2 }$ 
D)  $\pm 1 , \pm 11 , \pm \frac { 1 } { 2 } , \pm \frac { 11 } { 2 }$

Question 19

Find the zeros of the function.
-$$f ( x ) = 4 x ^ { 3 } + 36 x ^ { 2 } + 80 x$$

Accepted Answer

A)  0,5 , and 4 
B)  5 and 4 
C)  $- 5$ and $- 4$ 
D)  $0 , - 5$, and $- 4$ 
A)  0,5 , and 4 
B)  5 and 4 
C)  $- 5$ and $- 4$ 
D)  $0 , - 5$, and $- 4$

Question 20

Divide using synthetic division, and write a summary statement in fraction form.
-$\frac { 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 } { x - 1 }$

Accepted Answer

A) 
$2 x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + 4 x + 3 + \frac { 8 } { x - 1 }$ 
B) $$2 x ^ { 4 } + x ^ { 3 } - x ^ { 2 } + 2 x + 1 + \frac { 6 } { x - 1 }$$ 
C) 
$2 x ^ { 4 } - 3 x ^ { 3 } - x + \frac { 6 } { x - 1 }$ 
D) 
$2 x ^ { 4 } + x ^ { 3 } + 4 x ^ { 2 } + 3 x + \frac { 8 } { x - 1 }$ 
A) 
$2 x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + 4 x + 3 + \frac { 8 } { x - 1 }$ 
B) $$2 x ^ { 4 } + x ^ { 3 } - x ^ { 2 } + 2 x + 1 + \frac { 6 } { x - 1 }$$ 
C) 
$2 x ^ { 4 } - 3 x ^ { 3 } - x + \frac { 6 } { x - 1 }$ 
D) 
$2 x ^ { 4 } + x ^ { 3 } + 4 x ^ { 2 } + 3 x + \frac { 8 } { x - 1 }$

Describe the end behavior of the polynomial function by finding - $f ( x ) = ( x - 3 ) ( 1 - x ) ( 3 x - 5 )$

Find the axis of the graph of the function. - $f ( x ) = 4 x ^ { 2 } - 8 x + 9$

Graph the function. - $P(x)=(-2 x-1)(x+1)^{2}$ $Graph the function. - P(x)=(-2 x-1)(x+1)^{2}$

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = - 6 x ^ { 4 } + 5 x ^ { 2 } - 7$ - $f ( x ) = - 6 x ^ { 4 } + 5 x ^ { 2 } - 7$

Write a linear factorization of the function. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 x + 36$

Solve the problem. Round as appropriate. -The shadow cast by an object on a sunny day varies directly as the height of the object. If a person 76 inches tall casts a shadow 62 inches long, how tall is a tree which casts a shadow 31 feet in length?

Solve the polynomial inequality. - $2 x ^ { 3 } + 9 x ^ { 2 } - 38 x - 21 > 0$

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. - $k = 2 ; f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 2 x + 5$ ; Lower bound?

Solve the problem. -The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 31 t + 228$ . Determine the number of units to be sold in order for $\mathrm { P } = 0$ (the break- even point).

The polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$ measures the concentration of a dye in the bloodstream $x$ seconds after it is injected. Does the concentration increase between 10 and 11 seconds?

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. - $x - 4 ; 2 x ^ { 2 } - 14 x + 24$

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) = 1/x. - $f ( x ) = \frac { 6 x - 4 } { x - 3 }$

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 8 x + 11 ; k = - 2$

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { ( 2 x + 1 ) \sqrt { x - 2 } } { ( x - 8 ) ^ { 2 } }$

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Evaluate the limit based on the graph of f shown. - $Evaluate the limit based on the graph of f shown. - \lim _ { x \rightarrow } f ( x )$ $\lim _ { x \rightarrow } f ( x )$

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 11$

Find the zeros of the function. - $f ( x ) = 4 x ^ { 3 } + 36 x ^ { 2 } + 80 x$

Divide using synthetic division, and write a summary statement in fraction form. - $\frac { 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 } { x - 1 }$

Functions and Graphs

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 2: Polynomial, Power, and Rational Functions

Describe the end behavior of the polynomial function by finding - f(x)=(x−3)(1−x)(3x−5)f ( x ) = ( x - 3 ) ( 1 - x ) ( 3 x - 5 )f(x)=(x−3)(1−x)(3x−5)

Find the axis of the graph of the function. - f(x)=4x2−8x+9f ( x ) = 4 x ^ { 2 } - 8 x + 9f(x)=4x2−8x+9

Graph the function. - P(x)=(−2x−1)(x+1)2P(x)=(-2 x-1)(x+1)^{2}P(x)=(−2x−1)(x+1)2

Solve the problem. -The first column shows the independent variable (x)( \mathrm { x } )(x) . The second column shows the dependent variable (y). Use linear regression to predict the value of yyy when x=43x = 43x=43 .

Describe the end behavior of the polynomial function by finding - f(x)=−6x4+5x2−7f ( x ) = - 6 x ^ { 4 } + 5 x ^ { 2 } - 7f(x)=−6x4+5x2−7

Write a linear factorization of the function. - f(x)=x3+4x2+9x+36f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 x + 36f(x)=x3+4x2+9x+36