New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

College Algebra

by: Donny Graham

College Algebra MTH 103

Donny Graham
GPA 3.57

K. Park

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

K. Park
Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 7 page Class Notes was uploaded by Donny Graham on Saturday September 19, 2015. The Class Notes belongs to MTH 103 at Michigan State University taught by K. Park in Fall. Since its upload, it has received 13 views. For similar materials see /class/207305/mth-103-michigan-state-university in Mathematics (M) at Michigan State University.

Similar to MTH 103 at MSU

Popular in Mathematics (M)


Reviews for College Algebra


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/19/15
Section 22 More on Functions and Their Graphs Functions and Difference Quotient The expression f x h f x h for h at 0 is called the difference quotient Example 1 If fx 2x2 x 5 nd and simplify each expression a fx h b fxhhfx h 0 Piecewise Functions A function that is de ned by two or more equations over a speci ed domain is called a piecewise function Example 2 Use the function that describes the cellular phone plan 40 if 0 S t S 450 C0 40 045t 450 if t gt 450 to nd and interpret each of the following a C300 b CSOO Increasing and Decreasing Functions 1 A function is increasing on an open interval 1 if for any x1 and x2 in the interval where x1 lt x2 then fx1 lt fx2 2 A function is decreasing on an open interval 1 if for any x1 and x2 in the interval where x1 lt x2 then fx1 gt fx2 3 A function is constant on an open interval I if for any x1 and x2 in the interval where x1 ltx2then fx1fx2 L x I 39x Increasing Decreasing Constant Example 3 State Intervals on which the given function is increasing decreasing or constant Section 45 Exponential Growth and Decay Modeling Data Exponential Growth and Decay The mathematical model for exponential growth or decay is given by ft 1406 or A 1406 where 140 is the original amount or size at time t 0 A is the amount at time t and k is a constant representing the growth or decay rate If kgt 0 the function models the amount or size of a growing entity If klt 0 the function models the amount or size of a decaying entity Example 1 In 1990 the population of Africa was 643 million and by 2000 it had grown to 819 million a Use the exponential growth model A 1406 in which t is the number of years after 1990 to nd the exponential growth function that models the data b By which year will Africa s population reach 2000 million or two billion Section 34 Zeros of Polynomial Functions Rational Zero Theorem If a x aHxH a1x a0 has integer coefficient and E where g is reduced q q to lowest terms is rational zero of f then p is a factor of the constant term a0 q is a factor of the leading coef cient an Factors of a0 Possible rational zeros Factors of an Example 1 List all possible rational zeros of x3 2x2 5x 6 Example 2 List all possible rational zeros of 4x5 12x4 x 3 Finding Zeros of a Polynomial Function Step 1 List all possible rational zeros Step 2 Use synthetic division to nd a rational zero among the possibilities Step 3 Factor the polynomial using synthetic division Step 4 Repeat Step 1 through Step 3 until you get a quadratic factor Example 3 Find all zeros of x3 8x2 1 1x 20 Example 4 Find all zeros of x3 x2 5x 2 Example 5 Solve x4 6x3 22x2 30x 13 0 Section 13 Models and Application Problem Solving with Linear Equations Example 1 Basketball bicycle riding and football are the three sports and recreational activities in the United States In 2004 the number of injuries from basketball exceeded those from football by 06 million The number of injuries from bicycling exceeded those from football by 03 million Combined basketball bicycling and football accounted for 39 million injuries Determine the number of medically treated injuries from each of these recreational actives in 2004 Step 1 Read the problem carefully and state the problem in your own words Let x represent one of quantities in the problem Step 2 Represent other quantities in terms of x Step 3 Write an equation in x that models the conditions Step 4 Solve the equation and answer the question Step 5 Check your answer in the original wording of the problem Example 2 You are choosing between two longdistance telephone plans Plan A has a monthly fee of 15 with a charge of 008 per minute for all long distance calls Plan B has a monthly fee of 3 with a charge of 012 per minute for all longdistance calls For how many minutes of long distance calls will the costs for the two plans be the same Example 3 You inherited 5000 with the stipulation that for the rst year the money had to be invested in two funds paying 9 and 11 annual interest How much did you invest at each rate if the total interest earned for the year was 487


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Kyle Maynard Purdue

"When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the I made $280 on my first study guide!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.