1. Functions

2. What is a function? Machine with an input and output Output based on input Every input has only one output

3. Displaying Functions as Tables Given specific X-value Plug X-value into machine Y-value based on X and machine Put in table. Ex: Y=x+1

4. Displaying Functions as graphs Go left or right X-value From there Up and down y-value Connect dots Ex:

5. Domain & Range Domain: set of all x’s in the function Range: set of all y’s in the function Ex: Domain: (-∞, ∞) Range (-∞, ∞)

6. Is this a function? THIS IS NOTA FUNCTION This is a function

7. Is this a function? This is a function This is a function THIS IS NOTA FUNCTION

8. Zeros of a function When the function equals zero X+1=0 Zero when x=-1 When line cross x-axis Ex: Line crosses at -1

9. Combining functions All functions can be Added Subtracted Multiplied Divided Example: Y=(x+1)*(x-4) (x+3)+(x-7)

10. Transformations Transformations Move up and down Move left and right Grow and shrink Applicable to X and Y

11. Examples of Transformations Original y=x Transformation Y=2x+3

12. Examples of Transformations Original y=x2 Transformation Y=3x2

13. Slope and y-intercept Slope Many names: Rate of change Rise over run Y-Intercept Where line crosses y axis

14. How to find slope Rise over run= 2/1=2 Slope=2 Rise Run +2 +2 +2 +1 +1 +1

15. Y-Intercept How to find y-intercept Put in zero for x Outcome is answer Example Y=3x-4 Y=3(0)-4 Y=-4

16. Sources Benchmarks A 2.1 A 2.2 Photo sources http://www.flickr.com/photos/mikehamm/4425743870/ http://commons.wikimedia.org/wiki/File:Differentiable_function.png