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University of Louisiana at Lafayette - MATH 109 - Study Guide

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University of Louisiana at Lafayette - MATH 109 - Study Guide

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Math 109

Vojislav Petrovic

Fall 2014

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1. Domain zeros 96)

3 verheal Asyn 0 3.2cos-zeros of p(x)

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N=m N>m=y=0 oblique nist higher

- (x+3)2 (+12) (x)/x

Figure 1: Graph of P(x)

Exam 3 MW 2:30 PM

Name (Print): Michael Meric

Studyseven Don't forget about the age old question of What is the minus sign tells us?

If you want to learn more check out What is the proper definition of bedding?

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DIRECTIONS: Write your name clearly on the line above. Be as precise as you can in your answers. You must show all the work in order to receive full credit. Attempting a problem is encouraged and will usually result in some partial credit. If you want to learn more check out Who is the first president born west of the mississippi?

1. (a) Find a polynomial of lowest degree for which the graph would look like the graph

given in Figure 1.

1.- Even degree

Answer:

a

(negative)

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degree

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(b) Find a polynomial of lowest degree with real coefficients for which x = 2 - i is a

zero.

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Answer:

- 1

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C (-(2-1)(- (2:))

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x2 (2+1)x - (2-1) x + (2-1)(2+i) Y'ESADA 4 104 P(x) = (x2-4x+5

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Fall 2014 747 3:23

ja If you want to learn more check out What is one-to-one functions?

Vojislav Petrovic

Math 109

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or full

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2. Find all the zeros of the polynomial 2x+872 +7x+3. You must show all work for full

credit. Use of the calculator is for intuition, answer checking and simple calculations only. Answer:

13 12

7 3

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2 8 ? 2

2.

T -22 74=21

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1-2 + 122-(4) (2) (1)

2(2)-4

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3. Compute the following long division:

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2x3 - 2x2 + 3x - 1

2x + 4

x2-3x + 7.5

Answer:

2x - 2x + 3x - - (2x + 4x2)

- 6x + 3x - 1 - 6x2 - 12x

stud your

2x+4

15% -1 -x +30

3. Consider the following rational function:

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220

3x - 2

f(x) =

-3.- 4

(a) What (if any) are vertical asymptotes?

x - 3x-4

Answer.dy so

x=-||

.+1)=0/8= 4

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work

(b) What (if any) is the horizontal asymptote?

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Answer:

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Fall 2014

Math 109

Vojislav Petrovie

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x2 +2

2x2-3x-2

h

2-4 or 2x-450 2x = 4 + 2 = 13

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Figure 2: Graph of f(x)

(c) What are x-intercepts? y-intercept?

/ X-interceptas, 2 TY intercepts=05

Answer:

-2 = 5= yintercept

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(0)-360)-4

f(3999) =-3598; f (4.001) = 34901.9;

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(d) Determine limz4+ f(x), limz+4-f(x), lime--1- f(x) limx-_-1+ f(x), and sketch

the graph by using the coordinate system provided in Figure 2.

fel.oo)=601,28; 064

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x 4

f(x)

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4. The number N of long-distance phone calls per month (in million) between two cities

varies jointly as the populations P1 and P2 of the two citites (in million), and inversely as the distance between the two cities. If the number of long-distance phone calls is 30, for two cities of size 5 and 10 that are 180 miles apart, how many long-distance phone calls per month will be made between two cities of sixes 12 and 8 that are 300 miles apart?

Answer:

19

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10 15 2700

12 m) StudySoup

=30.180-1854

140.453-30-40-s

190

750

3600

= 24

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