1. Unit 2: Graphing Linear Equations and Inequalities

2. Introduction to Functions Section 1.7 PG 46

3. Coordinate Plane Vocabulary  2 lines that intersect at a right angle 1. Origin 2. Quadrant 1 (+,+) 3. Quadrant 2 (-, +) 4. Quadrant 3 (-, -) 5. Quadrant 4 (+, -) 6. X axis 7. Y axis

4. Vocab  Ordered pairs – a pair of #s used to identify a point in a plane  Relation – any set of ordered pairs (x,y)  Input/Domain – collection of all the input values or x- values  Output/Range – collection of all the output values or y- values

5. Function  a rule that establishes a relationship between 2 quantities (an input and an output).  Each input has one (and only one) output.  More than 1 input can have the same output. f Example: f(x)= x 2 + 1 Example: f(x)= x 2 + 1 f(2)= 2 2 + 1 f(2)= 5 f(2)= 2 2 + 1 f(2)= 5

6. You can view anything in the world as a function! Plant Mom

7. Input-Output Tables  For a relationship to be a function, it must be true that for each input, there is exactly one output.  To make your own input-output table, substitute the given input values into the given equation for x, then solve for y.

8. Examples  Determine whether each table represents a function. Explain. INPUTOUTPUT 17 28 39 410 INPUTOUTPUT 0-7 1 2-5 3-4 INPUTOUTPUT 14 25 26 37

9. Examples  Make an input-output table for the function. Use 0, 1, 2, 3 as the domain. INPUTOUTPUT INPUTOUTPUT INPUTOUTPUT

10. Keystone Application

11. CW  Pg. 49 # 1, 2, 4-7

12. HW  Pg. 49-50 #10-21, 25-26

13. Functions and Relations Section 4.8 PG 256

14. Review  A relation is a set of ordered pairs.  The set of all inputs or x-coordinates is called the Domain.  The set of all the outputs or y-coordinates is called the Range.  In order for a relation to be a function, every input (x- value) must correspond with exactly one output (y-value)

15. Examples  Decide whether the relation shown is a function. If it is, give the domain and range. Input 1 2 3 4 Output 2 4 5 Input 1 2 3 4 Output 5 7 9 Input 4 6 8 Output 0 1 4 4) Is the set of ordered pairs {(-4,1 ) (-3,2 ) ( -2,5) ( -1,1)} a function? InputOutput

16. Vertical Line Test  Used to determine whether or not a graph represents a function.  A graph represents a function if and only if no vertical line passes through two or more points on the graph. More Info...

17. Vertical Line Test

18. Video

19. Function Notation  The symbol f(x) replaces y  Stands for “the value of f at x”  Can be read simply as “f of x ”  You may also see g( x), h( x), etc. used instead of f(x )

20. Examples: Evaluate the function for the given value of the variable.

21. Examples:

22. CW  Pg 259 #1, 3-9

23. HW  Pg 259-260 #11-19 all 20-28 evens