CK12 - Trigonometry

Exponentialfunctions

havea variableas an

exponent.The graph

has a horizontal

asymptote.

As x approaches

, the function

valuesapproachthe

x-axis(y=0).

y= 2x,y= 3x, etc

Exponential

Theseare functions

that containfractions

with polynomials in

the numerator and

denominator. The

graphshavea hori-

zontaland a vertical

asymptote.

Asxapproaches±

, the y valuesap-

proach0 (the x-axis).

Asxapproaches1,

the y valuesapproach

±

, etc

Rational

All of thesefunctionscan be usedto representreal situations.For example,the linearfunctiony= 3xwas
usedaboveto representhow muchmoneyyou wouldmakesellingcandybars for $3.00each.This type of
situationis knownasdirectvariation.We say that the amountof moneyyou makevariesdirectlywith the
numberof candybars you sell. Directvariationbetweentwo variableswill alwaysbe modeledwith a linear
functionof the formy=mx. The slopeof the line,m, is the constantof variation.Noticethat the y-intercept
of the line is 0; that is, the line containsthe point(0,0).This makessensein termsof the candysellingsitu-
ation:if you sell 0 candybars,you make0 dollars.

Othersituationscan be modeledwith a differentkind of linearfunction.Considerthe followingsituation:a
restaurantis havinga special:a largecheesepizzacosts$8.00,and eachtoppingcosts$2.00.The cost of
a pizzacan be modeledwith the functionc(x) = 2x+ 8, wherexis the numberof toppingson the pizza.The
slopeof the line is 2, as eachtoppingadds$2 to the price.The y-interceptis 8: if you do not chooseany
additionaltoppings,the pizzacosts$8.00.

Quadratic,cubic,and otherpolynomialfunctionscan be usedto modelmanytypesof situationsAnother
importantfamilyof functionsis the rationalfunctions,or quotientsof polynomials,suchas: