Question 1

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { 5 x } { x ^ { 2 } - 1 }$

Accepted Answer

A)  $( 1,0 )$ 
B)  $( 5,0 )$ 
C)  $( - 1,0 ) , ( 1,0 )$ 
D)  $( 0,0 )$ 
A)  $( 1,0 )$ 
B)  $( 5,0 )$ 
C)  $( - 1,0 ) , ( 1,0 )$ 
D)  $( 0,0 )$

Question 2

Choose the one alternative that best completes the statement or answers the question.
-Economists use what is called a Leffer curve to predict the government revenue for tax rates from $0 \%$ to $100 \% .$ Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces t maximum revenue. Suppose an economist produces this rational function
$R ( x ) = \frac { 10 x ( 100 - x ) } { 50 + x }$, where $R$ is revenue in millions at a tax rate of $x$ percent. Use a graphing calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue?

Accepted Answer

A)  $41.2 \% ; \$ 264$ million 
B)  $34.0 \% ; \$ 271$ million 
C)  $36.6 \% ; \$ 268$ million 
D)  $35.8 \% ; \$ 276$ million 
A)  $41.2 \% ; \$ 264$ million 
B)  $34.0 \% ; \$ 271$ million 
C)  $36.6 \% ; \$ 268$ million 
D)  $35.8 \% ; \$ 276$ million

Question 3

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { x ^ { 2 } - 1 } { 2 + x ^ { 4 } }$

Accepted Answer

A)  $( 1,0 )$ 
B)  $( - 1,0 ) , ( 1,0 )$ 
C)  $( 2,0 )$ 
D)  none 
A)  $( 1,0 )$ 
B)  $( - 1,0 ) , ( 1,0 )$ 
C)  $( 2,0 )$ 
D)  none

Question 4

Choose the one alternative that best completes the statement or answers the question.
-The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled by the function, $C ( t ) = \frac { 12 t + 4 } { 3 t ^ { 2 } + 2 }$, where $t$ is the number of minutes after injection of the drug. When will the drug be at its highest concentration? Approximate your answer rounded to two decimal places.

Accepted Answer

A)  $t = 3.65$ minutes after the injection is given 
B)  $t = 4$ minutes after the injection is given 
C)  $\mathrm { t } = 0.55$ minutes after the injection is given 
D)  at the time of injection 
A)  $t = 3.65$ minutes after the injection is given 
B)  $t = 4$ minutes after the injection is given 
C)  $\mathrm { t } = 0.55$ minutes after the injection is given 
D)  at the time of injection

Question 5

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = - 14 x ^ { 3 } + 9 x ^ { 2 } - 7$

Accepted Answer

A)  Yes; degree 6 
B)  Yes; degree 5 
C)  Yes; degree 3 
D)  No; the last term has no variable 
A)  Yes; degree 6 
B)  Yes; degree 5 
C)  Yes; degree 3 
D)  No; the last term has no variable

Question 6

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
-$$f ( x ) = x ^ { 6 } + 4 x ^ { 5 } + 4 x ^ { 4 } + 3 x ^ { 3 } - x ^ { 2 } - 5 x + 4$$

Accepted Answer

A)  6 ; 2 or 0 positive zeros; 5,3 , or 1 negative zeros 
B)  6; 3 or 1 positive zeros; 4 , 2, or 0 negative zeros 
C)  6 ; 2 or 0 positive zeros; 4,2 , or 0 negative zeros 
D)  6; 4 , 2, or 0 positive zeros; 2, or 0 negative zeros 
A)  6 ; 2 or 0 positive zeros; 5,3 , or 1 negative zeros 
B)  6; 3 or 1 positive zeros; 4 , 2, or 0 negative zeros 
C)  6 ; 2 or 0 positive zeros; 4,2 , or 0 negative zeros 
D)  6; 4 , 2, or 0 positive zeros; 2, or 0 negative zeros

Question 7

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

Accepted Answer

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

Question 8

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$$

Accepted Answer

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

Question 9

Solve the inequality.
-$$\mathrm { x } ^ { 2 } - 36 \leq 0$$

Accepted Answer

A)  $[ - 9,9 ]$ 
B)  $[ - 6,6 ]$ 
C)  $( - \infty , - 9 ]$ or $[ 9 , \infty )$ 
D)  $( - \infty , - 3 ]$ or $[ 3 , \infty )$ 
A)  $[ - 9,9 ]$ 
B)  $[ - 6,6 ]$ 
C)  $( - \infty , - 9 ]$ or $[ 9 , \infty )$ 
D)  $( - \infty , - 3 ]$ or $[ 3 , \infty )$

Question 10

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$$

Accepted Answer

A)  x-intercepts: $- 3,2,3 ;$ y-intercept: 36 
B)  x-intercepts: $- 2 , - 9$; y-intercept: 18 
C)  $x$-intercepts: 2, 9; y-intercept: 18 
D)  $x$-intercepts: $- 3,2,3$; y-intercept: $- 36$ 
A)  x-intercepts: $- 3,2,3 ;$ y-intercept: 36 
B)  x-intercepts: $- 2 , - 9$; y-intercept: 18 
C)  $x$-intercepts: 2, 9; y-intercept: 18 
D)  $x$-intercepts: $- 3,2,3$; y-intercept: $- 36$

Question 11

Solve the inequality.
-$$( a + 4 ) ( a - 4 ) ( a - 5 ) > 0$$

Accepted Answer

A)  $( - \infty , 4 )$ 
B)  $( 5 , \infty )$ 
C)  $( - \infty , - 4 )$ or $( 4,5 )$ 
D)  $( - 4,4 )$ or $( 5 , \infty )$ 
A)  $( - \infty , 4 )$ 
B)  $( 5 , \infty )$ 
C)  $( - \infty , - 4 )$ or $( 4,5 )$ 
D)  $( - 4,4 )$ or $( 5 , \infty )$

Question 12

Write the word or phrase that best completes each statement or answers the question.
The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places.
-$x ^ { 3 } - 8 x - 3 = 0 ; - 1 \leq r \leq 0$

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }$$

Accepted Answer

A)  $x = y + 4$ 
B)  $y = x - 12$ 
C)  $y = x + 4$ 
D)  no oblique asymptotes 
A)  $x = y + 4$ 
B)  $y = x - 12$ 
C)  $y = x + 4$ 
D)  no oblique asymptotes

Question 14

Use the given zero to find the remaining zeros of the function.
-$$f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 19 x + 13 ; \text { zero: } - 3 + 2 i$$

Accepted Answer

A)  $- 3 - 2 \mathrm { i } , 1$ 
B)  $- 3 - 2 i , - 1$ 
C)  $2 - 3 \mathrm { i } , - 1$ 
D)  $2 - 3 i , 1$ 
A)  $- 3 - 2 \mathrm { i } , 1$ 
B)  $- 3 - 2 i , - 1$ 
C)  $2 - 3 \mathrm { i } , - 1$ 
D)  $2 - 3 i , 1$

Question 15

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = 4 x ^ { 4 } - 8 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 1$$

Accepted Answer

A)  $- 1,1 ; f ( x ) = ( x - 1 ) ( x + 1 ) \left( 4 x ^ { 2 } + 1 \right)$ 
B)  no real roots; $f ( x ) = \left( x ^ { 2 } + 1 \right) \left( 4 x ^ { 2 } + 1 \right)$ 
C)  $- 1$, multiplicity $2 ; f ( x ) = ( x + 1 ) ^ { 2 } \left( 4 x ^ { 2 } + 1 \right)$ 
D)  1 , multiplicity 2; $f ( x ) = ( x - 1 ) ^ { 2 } \left( 4 x ^ { 2 } + 1 \right)$ 
A)  $- 1,1 ; f ( x ) = ( x - 1 ) ( x + 1 ) \left( 4 x ^ { 2 } + 1 \right)$ 
B)  no real roots; $f ( x ) = \left( x ^ { 2 } + 1 \right) \left( 4 x ^ { 2 } + 1 \right)$ 
C)  $- 1$, multiplicity $2 ; f ( x ) = ( x + 1 ) ^ { 2 } \left( 4 x ^ { 2 } + 1 \right)$ 
D)  1 , multiplicity 2; $f ( x ) = ( x - 1 ) ^ { 2 } \left( 4 x ^ { 2 } + 1 \right)$

Question 16

Solve the equation in the real number system.
-$$3 x ^ { 3 } - x ^ { 2 } + 3 x - 1 = 0$$

Accepted Answer

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

Question 17

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.
-$$f ( x ) = x ^ { 3 } - 0.4 x ^ { 2 } - 2.5861 x + 3.0912$$

Accepted Answer

(a) For large values of @#LAT-DLM&, the graph of @#LAT-DLM&

Question 18

Solve the problem.
-Decide which of the rational functions might have the given graph.

Accepted Answer

A)  $f ( x ) = 1 - x$ 
B)  $f ( x ) = \frac { 1 } { x } - 1$ 
C) $ f ( x ) = 1 - \frac { 1 } { x }$ 
D)  $f ( x ) = 1 + \frac { 1 } { x }$ 
A)  $f ( x ) = 1 - x$ 
B)  $f ( x ) = \frac { 1 } { x } - 1$ 
C) $ f ( x ) = 1 - \frac { 1 } { x }$ 
D)  $f ( x ) = 1 + \frac { 1 } { x }$

Question 19

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x + 1 ) ( x - 6 ) ( x - 1 ) ^ { 2 }$$

Accepted Answer

A)  $x$-intercepts: $- 1,1,6$; $y$-intercept: 6 
B)  x-intercepts: $- 1,1,6$; $y$-intercept: $- 6$ 
C)  $x$-intercepts: $- 1,1 , - 6 ; y$-intercept: $- 6$ 
D)  $x$-intercepts: $- 1,1 , - 6 ; y$-intercept: 6 
A)  $x$-intercepts: $- 1,1,6$; $y$-intercept: 6 
B)  x-intercepts: $- 1,1,6$; $y$-intercept: $- 6$ 
C)  $x$-intercepts: $- 1,1 , - 6 ; y$-intercept: $- 6$ 
D)  $x$-intercepts: $- 1,1 , - 6 ; y$-intercept: 6

Question 20

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$$f ( x ) = 5 - \frac { 3 } { x ^ { 6 } }$$

Accepted Answer

A)  No; $x$ is raised to the negative 6 power 
B)  Yes; degree 6 
C)  Yes; degree $\frac { 1 } { 6 }$ 
D)  Yes; degree $- 6$ 
A)  No; $x$ is raised to the negative 6 power 
B)  Yes; degree 6 
C)  Yes; degree $\frac { 1 } { 6 }$ 
D)  Yes; degree $- 6$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { 5 x } { x ^ { 2 } - 1 }$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } - 1 } { 2 + x ^ { 4 } }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = - 14 x ^ { 3 } + 9 x ^ { 2 } - 7$

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - $f ( x ) = x ^ { 6 } + 4 x ^ { 5 } + 4 x ^ { 4 } + 3 x ^ { 3 } - x ^ { 2 } - 5 x + 4$

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

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$

Solve the inequality. - $\mathrm { x } ^ { 2 } - 36 \leq 0$

Find the x- and y-intercepts of f. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$

Solve the inequality. - $( a + 4 ) ( a - 4 ) ( a - 5 ) > 0$

Write the word or phrase that best completes each statement or answers the question. The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. - $x ^ { 3 } - 8 x - 3 = 0 ; - 1 \leq r \leq 0$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }$

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 19 x + 13 ; \text { zero: } - 3 + 2 i$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 4 x ^ { 4 } - 8 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 1$

Solve the equation in the real number system. - $3 x ^ { 3 } - x ^ { 2 } + 3 x - 1 = 0$

Solve the problem. -Decide which of the rational functions might have the given graph.

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 1 ) ( x - 6 ) ( x - 1 ) ^ { 2 }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 5 - \frac { 3 } { x ^ { 6 } }$

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 3: Polynomial and Rational Functions

Find the indicated intercept(s) of the graph of the function. - xxx -intercepts of f(x)=5xx2−1f ( x ) = \frac { 5 x } { x ^ { 2 } - 1 }f(x)=x2−15x​

Find the indicated intercept(s) of the graph of the function. - xxx -intercepts of f(x)=x2−12+x4f ( x ) = \frac { x ^ { 2 } - 1 } { 2 + x ^ { 4 } }f(x)=2+x4x2−1​

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x)=−14x3+9x2−7f ( x ) = - 14 x ^ { 3 } + 9 x ^ { 2 } - 7f(x)=−14x3+9x2−7

Graph the function. - f(x)=x+4xf(x)=x+\frac{4}{x}f(x)=x+x4​

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - f(x)=(x+14)4(x+1)5f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }f(x)=(x+41​)4(x+1)5

Solve the inequality. - x2−36≤0\mathrm { x } ^ { 2 } - 36 \leq 0x2−36≤0

Find the x- and y-intercepts of f. - f(x)=(x−2)2(x2−9)f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)f(x)=(x−2)2(x2−9)

Solve the inequality. - (a+4)(a−4)(a−5)>0( a + 4 ) ( a - 4 ) ( a - 5 ) > 0(a+4)(a−4)(a−5)>0

Write the word or phrase that best completes each statement or answers the question. The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. - x3−8x−3=0;−1≤r≤0x ^ { 3 } - 8 x - 3 = 0 ; - 1 \leq r \leq 0x3−8x−3=0;−1≤r≤0

Give the equation of the oblique asymptote, if any, of the function. - f(x)=x2+8x+5x+4f ( x ) = \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }f(x)=x+4x2+8x+5​

Use the given zero to find the remaining zeros of the function. - f(x)=x3+7x2+19x+13; zero: −3+2if ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 19 x + 13 ; \text { zero: } - 3 + 2 if(x)=x3+7x2+19x+13; zero: −3+2i

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - f(x)=4x4−8x3+5x2−2x+1f ( x ) = 4 x ^ { 4 } - 8 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 1f(x)=4x4−8x3+5x2−2x+1

Solve the equation in the real number system. - 3x3−x2+3x−1=03 x ^ { 3 } - x ^ { 2 } + 3 x - 1 = 03x3−x2+3x−1=0