1. Math I: Unit 1 Function Families Day 1 (8-15-11)
UNIT QUESTION: How do we graph functions, and what can be done to change the way they look?
Standard: MM1A1
Today’s Question:
What is a function?
Standard: MM1A1a, MM1A1b

2. Key Terms Relation – Any set of input that has an output
Function – Is a relation that every single input has exactly one output
Input (x-coordinate) is also called the Domain
Output (y-coordinate) is also called the Range

3. Making an Input-Output Table
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

4. Domain and Range Domain: {1, 2, 3, 4, 5, 6}

5. How do I know if it's a function?
Look at the input and output table – Each input must have exactly one output.
Look at the Graph – The Vertical Line test = NO vertical line can pass through two or more points on the graph

6. How do I know if it's a function?
Example 1:
{(3, 2), (4, 3), (5, 4), (6, 5)}
Example 2:
Reading the ordered pairs off of the graph, we get  {(2, 3), (2, 4), (3, 3), (4, 3)}

7. How do I know if it's a function?
Example 3:
Example 4:

8. How do I know if it's a function?
Example 5:
Example 6:

9. Function form of an equation
You have seen linear functions in the form
y = mx + b.
By naming a function f, you can write it using function notation: f(x) = mx + b
Function notation x-y notation
f(x) = 2x y = 2x + 3
f(x) = ½ x y = ½ x - 6

10. Evaluating a function f(x) = 2x – 3 when x = -2 and x = 3
= -4 – 3
= - 7
f(3) = ???

11. Evaluating a function f(x) = x2 – 2x + 3 when x = -3 and x = 4=
= 18
f(4) = ???

12. Name the function
f(x) = ???

13. Function and Mixed Review Practice
Homework
Function and Mixed Review Practice
f(x) = 2x + 5