1 / 25

Basic Functions

Basic Functions. Linear and Exponential Functions Power Functions Logarithmic Functions Trigonometric Functions. Linear Function. A population of 200 worms increases at the rate of 5 worms per day . How many worms are there after a fifteen days? . Linear Functions. Slope m=rise/run.

deacon
Download Presentation

Basic Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Basic Functions

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

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

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

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

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

  7. Exponential Growth • Population of Mexico City since 1980 (t=0) Is this a linear function?

  8. Equation from Table Initial Population t=0 Grows at 2.6% per year (100%+2.6% next period) 1.026 = growth factor 1=1+0.026 What is the doubling time?

  9. What do you need to know about the basic functions? • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Common domain • Intercepts • Dominance

  10. Power Functions

  11. Positive Even Powers • Shape • Domain • End behavior • Intercepts with coordinate axes

  12. Positive Odd Powers • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  13. Negative Even Powers • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  14. Negative Odd Powers • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  15. Positive Even Roots • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  16. Positive Odd Roots • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  17. Exponential Growth • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  18. Exponential Decay • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  19. Natural Log Function • Shape • Domain • End behavior • Intercepts with coordinate axes • Compare them • Intercepts • Dominance

  20. Sine and Cosine

  21. 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?

  22. Common domain Graphical Solution Algebraic Solution number line

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

More Related