A function is a machine that takes an input X and produces a single output Y. Functions can be displayed as tables by plugging in X values and listing the corresponding Y values. Functions can also be displayed as graphs by plotting the X and Y values and connecting the points. The domain is the set of all possible X values, while the range is the set of all possible Y values. A relation is only a function if each X value corresponds to a single Y value. The zeros of a function are the X values where the function equals 0. Functions can be combined, transformed, and have their slope and y-intercept calculated according to standard mathematical operations.

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.
X Y
Ex: 1 2
Y=x+1 2 3
3 4
4 5

4. Displaying Functions as graphs
Go left or right X-value
From there
Up and down y-value
Connect dots
Ex: X Y
1 2
2 3
3 4
4 5

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?
X Y X Y
2 3 2 3
4 3 2 4
5 2 3 6
7 8 4 7
This is a function THIS IS NOT A
FUNCTION

7. Is this a function?
This is a function
This is a function
THIS IS NOT A 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)

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

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

12. Examples of Transformations
Original Transformation
y=x2 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
Run Rise
X Y Slope=2
+1 1 5 +2
2 7
+1 +2
3 9
+1 4 11 +2

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/44
/
http://commons.wikimedia.org/wiki/File:Diff