Basic Functions

Linear and Exponential Functions Power Functions Logarithmic Functions Trigonometric Functions

A population of 200 worms increases at the rate of 5 worms per day. How many worms are there after a fifteen days? Linear Function

Linear Functions Slope m=rise/run Slope m=rise/run Change on y when x increases by 1 Y intercept or value when x=0

Exercise Find the equation of the line passing through the points (-2,1), (4,5) Point: Slope: Point-Slope form Slope-Y intercept form

Exponential Growth A population of 200 worms increases at the rate of 5% per day. How many worms are there after fifteen days?

Exponential Growth Population of Mexico City since 1980 (t=0) t (years after P(t) (in millions) Is this a linear function?

t (years after P(t) (in millions)

Equation from Table t (years after P(t) (in millions) Initial Population t=0 Grows at 2.6% per year (100%+2.6% next period) = growth factor 1= Grows at 2.6% per year (100%+2.6% next period) = growth factor 1= What is the doubling time?

1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Common domain – Intercepts – Dominance What do you need to know about the basic functions?

Power Functions

Positive Even Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes

Positive Odd Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Negative Even Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Negative Odd Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Positive Even Roots 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Positive Odd Roots 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Exponential Growth 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Exponential Decay 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Natural Log Function 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

Sine and Cosine

COMPARING FUNCTIONS Consider the functions For which values in their common domain is Toward the end points of the common domain which of the two functions dominate?

Common domain Graphical Solution Algebraic Solution number line

Dominance Comparing functions toward the end points of their common domains their common domains