Unit1.pdf

16 Pages
165 Views
Unlock Document

Department
Mathematics
Course
Mathematics 1225A/B
Professor
Vicki Olds
Semester
Winter

Description
Math1225ABUnit1ExponentialandLogarithmicFunctionstextreferenceSections51and52mixedtogethercustomtextpgs319cVOlds2012Unit111ExponentialandLogarithmicFunctionsWestartthecoursewithareviewofexponentialandlogarithmicfunctionsandtheirpropertiesTheninthenextunitwewillinthecontextofthesekindsoffunctionsreviewwhatyoulearnedinIntroductoryCalculusthevariousdierentiationrulesaswellasusingcalculusforgraphingandalsotheconceptsofimplicitandlogarithmicdierentiationExponentialFunctionsxDenition11Thefunctionfxbwithb0andb1iscalledtheexponentialfunctionwithbasebThatiseverypositivenumberotherthan1isthebaseofanexponentialfunctionandthevariableinthefunctionistheexponentiethepowertowhichthebaseisraisedRecallthatthedomainofafunctionfxisthesetofallxvaluesforwhichthatfunctionisxdenedForanyb0withb1thefunctionfxbisdenedeverywhereieforallrealvaluesofxThereforethedomainofanyexponentialfunctionisthesetofallrealnumbersietheintervalSimilarlyrecallthattherangeofafunctionfxisthesetofallvalueswhichthefunctionhasanywhereinitsdomainThatisforyfxtherangeisthesetofyvalueswhichcanoccurForanyexponentialfunctionwhenapositivebaseisraisedtoanypowernomatterwhetherpositiveornegativeintegerorotherwisetheresultisalwaysapositivenumberThatiswhenb0andxb1thevalueofbisalwayspositivenomatterwhatthevalueofxisAndanypositivevaluecanbeobtainedsotherangeofanyexponentialfunctionisthesetofallpositiverealnumbersietheinterval0GraphsofExponentialFunctionsxForanyb1thegraphofyblookslikethegraphinFigure1belowNoticethatthisgraphisincreasingthroughoutitsdomainisconcaveupwardeverywhereandpassesthroughthepoint01xxAlsonoticethattheliney0isahorizontalasymptotewithlimb0whilelimbxxFigure1Anexponentialfunctionwithbaseb1
More Less

Related notes for Mathematics 1225A/B

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit