1. Basic Functions

2. Linear and Exponential Functions Power Functions Logarithmic Functions Trigonometric Functions

3. 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

4. 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

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

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

8. Exponential Growth Population of Mexico City since 1980 (t=0) t (years after 1980 0123 P(t) (in millions) 67.3870.918782172.762670574.6544999 Is this a linear function?

9. t (years after 1980 0123 P(t) (in millions) 67.3870.918782172.762670574.6544999

10. Equation from Table t (years after 1980 0123 P(t) (in millions) 67.3870.918782172.762670574.6544999 Initial Population t=0 Grows at 2.6% per year (100%+2.6% next period) 1.026 = growth factor 1=1+0.026 Grows at 2.6% per year (100%+2.6% next period) 1.026 = growth factor 1=1+0.026 What is the doubling time?

11. 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?

12. Power Functions

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

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

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

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

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

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

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

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

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

22. Sine and Cosine

23. 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?

24. Common domain Graphical Solution Algebraic Solution number line

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