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

Col Alg for Math,Science,Engin

by: August Feeney

Col Alg for Math,Science,Engin MTH 111C

Marketplace > Portland Community College > Math > MTH 111C > Col Alg for Math Science Engin
August Feeney
GPA 3.98


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

Class Notes
25 ?




Popular in Course

Popular in Math

This 5 page Class Notes was uploaded by August Feeney on Monday October 19, 2015. The Class Notes belongs to MTH 111C at Portland Community College taught by Staff in Fall. Since its upload, it has received 40 views. For similar materials see /class/224641/mth-111c-portland-community-college in Math at Portland Community College.

Similar to MTH 111C at PCC


Reviews for Col Alg for Math,Science,Engin


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: 10/19/15
Haberman King MTH 1110 Section IV Power Polynomial and Rational Functions Module 1 Power Functions DEFINITION A power function is a function of the form fx kxP where k and p are constants EXAMPLE Which of the following functions are power functions For each power function state the value of the constants k and p in the formula y kxP a bx 5x 34 b mx 74 c lx32x cl sx Z5 SOLUTIONS a The function bx 5x 34 is not a power function because we cannot write it in the form y kxP bThe function mx 74 is a power function because we can rewrite its formula as mx7x14 Sok7 and p c The function 1x 32x is not a power function because the power is not constant In fact 1x 32x is an exponential function J7 xSZ 7x752 cl Since we see that sx can be written in the form y kxP where k J7 and x p so s is a power function a primer functmn we can nd tne tune un s tunnu1a are untne graph uf afu ctm t 5 EXAMPLE Suppuset att e pumts 1 81 and 3729 Fwd an a1gebra1e nuetur assummgthau 1 a ah earfu mu b an expunentta1 tunetmn c a primer tunetmn SOLUT ONS 1t 1s a h earfu ctm W a e k uvvt at ts ru1e nastunn fx 7 mx b We can use tne fur m Wu gwe pumtstu s we Sn uvvvve k uvvt at x 7 324K 5 We can use etnerune uttne gwen pmntstu nd A Let suse 181 1 81 2 1 7 817 3241 5 2 b 7 817 324 2 b 7 7 243 Thus w 1 nean ts ru1e 1 x 7 324K 7 243 V f 1 an expunent1a1 funmun We knew 1ts ru1e nas tunn fx 7 abx We can use tne Wu gwen pmntstu nd Wu Equatmns 1nvu1v1ng nd 5 1 81 2 1 7 817 115 3 729 2 3 7 729 7 ab 1mHa systems uf edua uns by furmmg ratms Let s b 1n Seetmn 1H Mudu1e 2 we sawed s r try a d erent rnetnud nere tne subs tu on rnetnu Let s start by SEIMng tne rst Equatmn fur a 817 115 0 Now we can substitute the expression for a in the second equation 729ab3 2 729b3 2 72981b2 2 3 81 b 3 912 3 b J5 3 we don39t need ixg since the base ofan exponential function is always positive Now that we know what b is we can use the fact that a to find a Thus if f is exponential its rule is fx 273 Since f is a power function we know that its rule has form fx kxp We can use the two given points to find two equations involving k and p 1 81 2 f1 81 k1P 3 729 2 f3 729 k3P We can use the first equation to immediately find k 81k1P 3 k 81 Now we can find p by substituting k 81 into the second equation 729813P E P 3 81 3 note that this could be solved with logarithms P 3 9 3 ifthe solution weren39t so obvious 3 p2 Thus if f is a power function its rule is fx 81x2 Graphs of Power Functions For a power function y kxp the greater the power of p the faster the outputs grow Below are the graphs of six power functions Notice that as the power increases the outputs increase more and more quickly As x increases without bound written Jr gt00quot higher powers of x get a lot larger than ie dominate lower powers of x Note that we are discussing the longterm behavior of the function 1 2 3 4 32 yzxzayzxi yX4 yzxsi The graphs of y x y x As x approaches zero written quotx gt0quot the story is completely different If x is between 0 and 1 x3 is largerthan x4 which is largerthan x5 Try x 01 to confirm this For values of x near zero smaller powers dominate On the graph below notice how on the interval 0 1 the linear power function y x dominates power functions of larger power 1 Thegraphsofyx yx32 yx2yx3 yx yx EXAMPLE Use your graohhg eateutator to graph fx 1000 and w x tor x gt 0 Cumpare the Dngrterm behavmr or these two ruhotohs cum HERE BE sure to turn up the yo1urhe on your cumputer Cou1o the graph or x1000gt and g x e x gt10007 Tu oete h e x hterseot agam tor sorhe ya1ue rmmE vmere tese graphs mters or BEL 1et s so1ye the Equatmn x 0 x g0 L1000x3 0 31000 shoe the oh1y x 1000 hterseot when x gt 1000 so1ut1ohs to m Equatmn are F0 a o F1000 the graph or and g ohty hterseot at F0 and F1000 so they do not EXAMPLE Use your graohhg eateutator to graph the oowertuhouoh fx x3 and the exoohehttat fun m gltxgt 2 tor x gt 0 Compare the ungrterm behavmr these WEI funmuns DUCK HERE amp Kev Poim39 Ahy pusmve mErEaSmg exooheht1a1 tuhmoh eyehtuauy gruvvs taster thah anypEIWErfunmun


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

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Janice Dongeun University of Washington

"I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

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.