Question 1

Find the remainder when f(x) is divided by (x - k)
-$$f ( x ) = x ^ { 2 } + 3 x - 7 ; k = - 4$$

Accepted Answer

A)  21 
B)  35 
C)  $- 3$ 
D)  11 
A)  21 
B)  35 
C)  $- 3$ 
D)  11

Question 2

Find the zeros of the function.
-$$f ( x ) = 3 x ^ { 3 } - 11 x ^ { 2 } - 4 x$$

Accepted Answer

A)  $- \frac { 1 } { 3 }$ and 4 
B)  $0 , - \frac { 1 } { 3 }$, and $- 4$ 
C)  $0 , - \frac { 1 } { 3 }$, and 4 
D)  $- \frac { 1 } { 3 }$ and $- 4$ 
A)  $- \frac { 1 } { 3 }$ and 4 
B)  $0 , - \frac { 1 } { 3 }$, and $- 4$ 
C)  $0 , - \frac { 1 } { 3 }$, and 4 
D)  $- \frac { 1 } { 3 }$ and $- 4$

Question 3

Match the polynomial function graph to the appropriate zeros and multiplicities.
-

Accepted Answer

A)  $- 2$ (multiplicity 3), 4 (multiplicity 2) 
B)  -2 (multiplicity 3), 4 (multiplicity 3) 
C)  $- 2$ (multiplicity 2), 4 (multiplicity 2 ) 
D)  $- 2$ (multiplicity 2), 4 (multiplicity 3 ) 
A)  $- 2$ (multiplicity 3), 4 (multiplicity 2) 
B)  -2 (multiplicity 3), 4 (multiplicity 3) 
C)  $- 2$ (multiplicity 2), 4 (multiplicity 2 ) 
D)  $- 2$ (multiplicity 2), 4 (multiplicity 3 )

Question 4

Write the statement as a power function equation. Use k as the constant of variation.
-The cost c of a turkey varies directly as its weight w.

Accepted Answer

A)  $c = \frac { w } { k }$ 
B)  $\mathrm { c } = \mathrm { kw } ^ { 2 }$ 
C)  $\mathrm { c } = \frac { \mathrm { k } } { \mathrm { w } }$ 
D)  $\mathrm { c } = \mathrm { kw }$ 
A)  $c = \frac { w } { k }$ 
B)  $\mathrm { c } = \mathrm { kw } ^ { 2 }$ 
C)  $\mathrm { c } = \frac { \mathrm { k } } { \mathrm { w } }$ 
D)  $\mathrm { c } = \mathrm { kw }$

Question 5

Evaluate the limit based on the graph of f shown.
- 
$$\lim _ { x \rightarrow 3 ^ { - } } f ( x )$$

Accepted Answer

A)  3 
B)  $=$ 
C)  0 
D)  $\infty$ 
A)  3 
B)  $=$ 
C)  0 
D)  $\infty$

Question 6

Use the graph to guess possible linear factors of f(x). Then completely factor f(x) with the aid of synthetic division.
-$f(x)=7 x^{3}-39 x^{2}-40 x+132$

Accepted Answer

A)  $f ( x ) = ( x + 2 ) ( x - 6 ) ( 7 x - 11 )$ 
B)  $f ( x ) = ( x - 2 ) ( x + 6 ) ( 7 x + 11 )$ 
C)  $f ( x ) = ( x + 2 ) ( x - 6 ) ( 7 x - 13 )$ 
D)  $f ( x ) = ( x - 2 ) ( x + 6 ) ( 7 x + 13 )$ 
A)  $f ( x ) = ( x + 2 ) ( x - 6 ) ( 7 x - 11 )$ 
B)  $f ( x ) = ( x - 2 ) ( x + 6 ) ( 7 x + 11 )$ 
C)  $f ( x ) = ( x + 2 ) ( x - 6 ) ( 7 x - 13 )$ 
D)  $f ( x ) = ( x - 2 ) ( x + 6 ) ( 7 x + 13 )$

Question 7

State the power and constant of variation for the function, and then analyze it.
-$$f ( x ) = - 3 x ^ { 4 }$$

Accepted Answer

Power is 4 ; constant of variation is @#LAT-DLM&;

Question 8

Use limits to describe the behavior of the rational function near the indicated asymptote.
-$$f ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }$$
Describe the behavior of the function near its vertical asymptotes.

Accepted Answer

A)  $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = - \infty$ 
B)  $\operatorname { lim~ } _ { x \rightarrow \theta ^ { - } } f ( x ) = 0 , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = - \infty , \quad \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty$ 
C)  $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty$ 
D)  $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = \infty , \lim _ { x \rightarrow \mathbb { Z } ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty$ 
A)  $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = - \infty$ 
B)  $\operatorname { lim~ } _ { x \rightarrow \theta ^ { - } } f ( x ) = 0 , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = - \infty , \quad \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty$ 
C)  $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty$ 
D)  $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = \infty , \lim _ { x \rightarrow \mathbb { Z } ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty$

Question 9

Describe how to transform the graph of an appropriate monomial function f(x) = xn into the graph of the given
polynomial function. Then sketch the transformed graph.
-$$g ( x ) = \frac { 5 } { 3 } ( x - 5 ) ^ { 3 } + 4$$

Accepted Answer

Obtain the graph of @#LAT-DLM& by shifti

Question 10

Write the polynomial in standard form and identify the zeros of the function.
-$$f ( x ) = ( x - 1 ) ( x - \sqrt { 7 } i ) ( x + \sqrt { 7 } i )$$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 7 x - 7 ;$ zeros $1 , \pm \sqrt { 7 } i$ 
B)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + 7 ; \operatorname { zeros } 1 , \pm \sqrt { 7 } i$ 
C)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 49 x - 49$; zeros $1 , \pm 7 i$ 
D)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + 7 ;$ zeros $- 1 , \pm \sqrt { 7 } i$ 
A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 7 x - 7 ;$ zeros $1 , \pm \sqrt { 7 } i$ 
B)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + 7 ; \operatorname { zeros } 1 , \pm \sqrt { 7 } i$ 
C)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 49 x - 49$; zeros $1 , \pm 7 i$ 
D)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + 7 ;$ zeros $- 1 , \pm \sqrt { 7 } i$

Question 11

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 $x = 41$.

Accepted Answer

A)  $126.68$ 
B)  $118.48$ 
C)  $130.78$ 
D)  $138.98$ 
A)  $126.68$ 
B)  $118.48$ 
C)  $130.78$ 
D)  $138.98$

Question 12

Provide an appropriate response.
-Fill in the blanks to complete the statement. A polynomial function of degree 11 has at least $x$-intercept(s) and at most $\quad x$-intercept(s).

Accepted Answer

A)  $11 ; 11$ 
B)  $0 ; 10$ 
C)  $10 ; 11$ 
D)  $1 ; 11$ 
A)  $11 ; 11$ 
B)  $0 ; 10$ 
C)  $10 ; 11$ 
D)  $1 ; 11$

Question 13

Solve the problem.
-Dan's long-distance phone carrier charges him $\$ 6.95$ a month for service. In addition, Dan is charged 12 cents a minute for the calls he makes. If his monthly bill is $\$ 35.87$, how many minutes of calls did he make?

Accepted Answer

A)  252 minutes 
B)  231 minutes 
C)  242 minutes 
D)  241 minutes 
A)  252 minutes 
B)  231 minutes 
C)  242 minutes 
D)  241 minutes

Question 14

For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { 2 x ^ { 2 } - 8 x - 3 } { 9 x ^ { 2 } - 7 x + 7 }$, horizontal

Accepted Answer

A)  $y = 8 / 7$ 
B)  $y = 0$ 
C)  $y = 2 / 9$ 
D)  None 
A)  $y = 8 / 7$ 
B)  $y = 0$ 
C)  $y = 2 / 9$ 
D)  None

Question 15

Use limits to describe the behavior of the rational function near the indicated asymptote.
-$$f ( x ) = \frac { 4 x ^ { 2 } - 3 } { x ^ { 2 } + 1 }$$
Describe the behavior of the function near its horizontal asymptote (the end behavior).

Accepted Answer

A)  $\lim _ { x \rightarrow \infty } f ( x ) = 0 , \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = 4 , \lim _ { x \rightarrow \infty } f ( x ) = 4$ 
C) 
  
D)  $\lim _ { x \rightarrow 1 ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow 1 ^ { + } } f ( x ) = \infty$ 
A)  $\lim _ { x \rightarrow \infty } f ( x ) = 0 , \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = 4 , \lim _ { x \rightarrow \infty } f ( x ) = 4$ 
C) 
  
D)  $\lim _ { x \rightarrow 1 ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow 1 ^ { + } } f ( x ) = \infty$

Question 16

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative.
-$$f ( x ) = ( x - 7 ) ( 3 x + 5 ) ( x + 2 )$$

Accepted Answer

A)  (a) $\left\{ - 2 , - \frac { 5 } { 3 } , 7 \right\}$, (b) $( \infty , - 2 ) \cup \left( - \frac { 5 } { 3 } , 7 \right)$, (c) $\left( - 2 , - \frac { 5 } { 3 } \right) \cup ( 7 , \infty )$ 
B)  (a) $\left\{ - 2 , - \frac { 5 } { 3 } , 7 \right\}$ (b) $\left( - 2 , - \frac { 5 } { 3 } \right) \cup ( 7 , \infty )$, (c) $( \infty , - 2 ) \cup \left( - \frac { 5 } { 3 } , 7 \right)$ 
C)  (a) $\{ - 2 , - 5,7 \rangle$, (b) $( - 2 , - 5 ) \cup ( 7 , \infty )$, (c) $( \infty , - 2 ) \cup ( - 5,7 )$ 
D)  (a) $\left\{ - 2 , - \frac { 5 } { 3 } , 7 \right\}$ (b) $( - 2,7 )$, (c) $( * , - 2 ) \cup ( 7 , \infty )$ 
A)  (a) $\left\{ - 2 , - \frac { 5 } { 3 } , 7 \right\}$, (b) $( \infty , - 2 ) \cup \left( - \frac { 5 } { 3 } , 7 \right)$, (c) $\left( - 2 , - \frac { 5 } { 3 } \right) \cup ( 7 , \infty )$ 
B)  (a) $\left\{ - 2 , - \frac { 5 } { 3 } , 7 \right\}$ (b) $\left( - 2 , - \frac { 5 } { 3 } \right) \cup ( 7 , \infty )$, (c) $( \infty , - 2 ) \cup \left( - \frac { 5 } { 3 } , 7 \right)$ 
C)  (a) $\{ - 2 , - 5,7 \rangle$, (b) $( - 2 , - 5 ) \cup ( 7 , \infty )$, (c) $( \infty , - 2 ) \cup ( - 5,7 )$ 
D)  (a) $\left\{ - 2 , - \frac { 5 } { 3 } , 7 \right\}$ (b) $( - 2,7 )$, (c) $( * , - 2 ) \cup ( 7 , \infty )$

Question 17

List the x- and y-intercepts, and graph the function.
-$$f ( x ) = \frac { x - 1 } { x ^ { 2 } - 6 x - 7 }$$

Accepted Answer

A)  x-intercept: $( 1,0 ) , y$-intercept: $\left( 0 , - \frac { 1 } { 7 } \right)$;
  
B)  x-intercept: $( 1,0 ) , \mathrm { y }$-intercept: $\left( 0 , \frac { 1 } { 7 } \right)$;
  
C)  $x$-intercept: $( - 1,0 ) , y$-intercept: $\left( 0 , - \frac { 1 } { 15 } \right)$;
  
D)  $x$-intercept: $( - 1,0 ) , y$-intercept: $\left( 0 , \frac { 1 } { 15 } \right)$;
  
A)  x-intercept: $( 1,0 ) , y$-intercept: $\left( 0 , - \frac { 1 } { 7 } \right)$;
  
B)  x-intercept: $( 1,0 ) , \mathrm { y }$-intercept: $\left( 0 , \frac { 1 } { 7 } \right)$;
  
C)  $x$-intercept: $( - 1,0 ) , y$-intercept: $\left( 0 , - \frac { 1 } { 15 } \right)$;
  
D)  $x$-intercept: $( - 1,0 ) , y$-intercept: $\left( 0 , \frac { 1 } { 15 } \right)$;

Question 18

Divide f(x) by d(x), and write a summary statement in the form indicated.
-$f ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } - 5 x + 4 ; d ( x ) = 2 x + 1 \quad$ (Write answer in polynomial form)

Accepted Answer

A)  $f ( x ) = ( 2 x + 1 ) \left( 2 x ^ { 2 } - 7 x + 1 \right) - 3$ 
B)  $f ( x ) = ( 2 x + 1 ) \left( - 2 x ^ { 2 } - 7 x + 1 \right) + 3$ 
C)  $f ( x ) = ( 2 x + 1 ) \left( 2 x ^ { 2 } - 7 x + 1 \right) + 3$ 
D)  $f ( x ) = ( 2 x + 1 ) \left( 2 x ^ { 2 } - 5 x + 1 \right) + 3$ 
A)  $f ( x ) = ( 2 x + 1 ) \left( 2 x ^ { 2 } - 7 x + 1 \right) - 3$ 
B)  $f ( x ) = ( 2 x + 1 ) \left( - 2 x ^ { 2 } - 7 x + 1 \right) + 3$ 
C)  $f ( x ) = ( 2 x + 1 ) \left( 2 x ^ { 2 } - 7 x + 1 \right) + 3$ 
D)  $f ( x ) = ( 2 x + 1 ) \left( 2 x ^ { 2 } - 5 x + 1 \right) + 3$

Question 19

Write the word or phrase that best completes each statement or answers the question.
Write a sentence that expresses the relationship in the formula, using the language of variation or proportion.
-$$\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh } , \text { where } \mathrm { A } \text { is the area of a triangle with given base and height }$$

Accepted Answer

The area of a triang

Question 20

Solve the problem.
-The stadium vending company finds that sales of hot dogs average 45,000 hot dogs per game when the hot dogs sell for $\$ 2.50$ each. For each 25 cent increase in the price, the sales per game drop by 2000 hot dogs. Determine a function $R ( x )$ that models the total revenue per game, where $x$ is the number of $\$ 0.25$ increases in the price of a hot dog.

Accepted Answer

A)  $R ( x ) = - 500 x ^ { 2 } + 6250 x + 112,500$ 
B)  $R ( x ) = 500 x ^ { 2 } + 6250 x - 112,500$ 
C)  $R ( x ) = - 500 x ^ { 2 } + 14,250 x + 112,500$ 
D)  $R ( x ) = - 500 x ^ { 2 } + 11,250 x + 112,500$ 
A)  $R ( x ) = - 500 x ^ { 2 } + 6250 x + 112,500$ 
B)  $R ( x ) = 500 x ^ { 2 } + 6250 x - 112,500$ 
C)  $R ( x ) = - 500 x ^ { 2 } + 14,250 x + 112,500$ 
D)  $R ( x ) = - 500 x ^ { 2 } + 11,250 x + 112,500$

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = x ^ { 2 } + 3 x - 7 ; k = - 4$

Find the zeros of the function. - $f ( x ) = 3 x ^ { 3 } - 11 x ^ { 2 } - 4 x$

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Write the statement as a power function equation. Use k as the constant of variation. -The cost c of a turkey varies directly as its weight w.

Evaluate the limit based on the graph of f shown. - $Evaluate the limit based on the graph of f shown. - \lim _ { x \rightarrow 3 ^ { - } } f ( x )$ $\lim _ { x \rightarrow 3 ^ { - } } f ( x )$

State the power and constant of variation for the function, and then analyze it. - $f ( x ) = - 3 x ^ { 4 }$

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }$ Describe the behavior of the function near its vertical asymptotes.

Write the polynomial in standard form and identify the zeros of the function. - $f ( x ) = ( x - 1 ) ( x - \sqrt { 7 } i ) ( x + \sqrt { 7 } i )$

Provide an appropriate response. -Fill in the blanks to complete the statement. A polynomial function of degree 11 has at least $x$ -intercept(s) and at most $\quad x$ -intercept(s).

Solve the problem. -Dan's long-distance phone carrier charges him $\$ 6.95$ a month for service. In addition, Dan is charged 12 cents a minute for the calls he makes. If his monthly bill is $\$ 35.87$ , how many minutes of calls did he make?

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { 2 x ^ { 2 } - 8 x - 3 } { 9 x ^ { 2 } - 7 x + 7 }$ , horizontal

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { 4 x ^ { 2 } - 3 } { x ^ { 2 } + 1 }$ Describe the behavior of the function near its horizontal asymptote (the end behavior).

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - $f ( x ) = ( x - 7 ) ( 3 x + 5 ) ( x + 2 )$

List the x- and y-intercepts, and graph the function. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 6 x - 7 }$ $List the x- and y-intercepts, and graph the function. - f ( x ) = \frac { x - 1 } { x ^ { 2 } - 6 x - 7 }$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } - 5 x + 4 ; d ( x ) = 2 x + 1 \quad$ (Write answer in polynomial form)

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

Find the remainder when f(x) is divided by (x - k) - f(x)=x2+3x−7;k=−4f ( x ) = x ^ { 2 } + 3 x - 7 ; k = - 4f(x)=x2+3x−7;k=−4

Find the zeros of the function. - f(x)=3x3−11x2−4xf ( x ) = 3 x ^ { 3 } - 11 x ^ { 2 } - 4 xf(x)=3x3−11x2−4x

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Write the statement as a power function equation. Use k as the constant of variation. -The cost c of a turkey varies directly as its weight w.

Evaluate the limit based on the graph of f shown. - lim⁡x→3−f(x)\lim _ { x \rightarrow 3 ^ { - } } f ( x )limx→3−​f(x)

Use the graph to guess possible linear factors of f(x). Then completely factor f(x) with the aid of synthetic division. - f(x)=7x3−39x2−40x+132f(x)=7 x^{3}-39 x^{2}-40 x+132f(x)=7x3−39x2−40x+132

State the power and constant of variation for the function, and then analyze it. - f(x)=−3x4f ( x ) = - 3 x ^ { 4 }f(x)=−3x4

Use limits to describe the behavior of the rational function near the indicated asymptote. - f(x)=x+1x2−2xf ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }f(x)=x2−2xx+1​ Describe the behavior of the function near its vertical asymptotes.

Describe how to transform the graph of an appropriate monomial function f(x) = xn into the graph of the given polynomial function. Then sketch the transformed graph. - g(x)=53(x−5)3+4g ( x ) = \frac { 5 } { 3 } ( x - 5 ) ^ { 3 } + 4g(x)=35​(x−5)3+4

Write the polynomial in standard form and identify the zeros of the function. - f(x)=(x−1)(x−7i)(x+7i)f ( x ) = ( x - 1 ) ( x - \sqrt { 7 } i ) ( x + \sqrt { 7 } i )f(x)=(x−1)(x−7​i)(x+7​i)

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=41x = 41x=41 .

Provide an appropriate response. -Fill in the blanks to complete the statement. A polynomial function of degree 11 has at least xxx -intercept(s) and at most x\quad xx -intercept(s).

Solve the problem. -Dan's long-distance phone carrier charges him $6.95\$ 6.95$6.95 a month for service. In addition, Dan is charged 12 cents a minute for the calls he makes. If his monthly bill is $35.87\$ 35.87$35.87 , how many minutes of calls did he make?

For the given function, find all asymptotes of the type indicated (if there are any) - f(x)=2x2−8x−39x2−7x+7f ( x ) = \frac { 2 x ^ { 2 } - 8 x - 3 } { 9 x ^ { 2 } - 7 x + 7 }f(x)=9x2−7x+72x2−8x−3​ , horizontal

Use limits to describe the behavior of the rational function near the indicated asymptote. - f(x)=4x2−3x2+1f ( x ) = \frac { 4 x ^ { 2 } - 3 } { x ^ { 2 } + 1 }f(x)=x2+14x2−3​ Describe the behavior of the function near its horizontal asymptote (the end behavior).

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - f(x)=(x−7)(3x+5)(x+2)f ( x ) = ( x - 7 ) ( 3 x + 5 ) ( x + 2 )f(x)=(x−7)(3x+5)(x+2)

List the x- and y-intercepts, and graph the function. - f(x)=x−1x2−6x−7f ( x ) = \frac { x - 1 } { x ^ { 2 } - 6 x - 7 }f(x)=x2−6x−7x−1​

Divide f(x) by d(x), and write a summary statement in the form indicated. - f(x)=4x3−12x2−5x+4;d(x)=2x+1f ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } - 5 x + 4 ; d ( x ) = 2 x + 1 \quadf(x)=4x3−12x2−5x+4;d(x)=2x+1 (Write answer in polynomial form)