Functions vs Relations Relation Any set of input

Functions vs Relations

Relation • Any set of input that has an output

Function • A relation where EACH input has exactly ONE output • Each element from the domain is paired with one and only one element from the range

Domain • x – coordinates • Independent variable • Input

Range • y – coordinates • Dependent variable • Output

Revisit the warm up: • It’s Hat Day at the Braves game and every child 10 years old and younger gets a team Braves hat at Gate 7. The policies at the game are very strict. ▫ ▫ Every child entering Gate 7 must get a hat. Every child entering Gate 7 must wear the hat. Only children age 10 or younger can enter Gate 7. No child shall wear a different hat than the one given to them at the gate. 1. What is the gate’s input? Going in: Children 10 & younger without 2. hats What is the gate’s output? Coming out of Gate 7: Children 10 & younger WITH hats

How do I know 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

Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)} A = Function B = Relation function

Example 2: function

Example 3: relation

Example 4: ( x, y) = (student’s name, shirt color) function

Example 5: Red Graph relation

Example 6 Jacob Angela Nick Greg Tayla Trevor Honda Toyota Ford function

Example 7 A person’s cell phone number versus their name. function

Function Notation

Function form of an equation • A way to name a function • f(x) is a fancy way of writing “y” in an equation. • Pronounced “f of x”

Evaluating Functions

8. Evaluating a function Tell me what you get f(x) = 2 x – 3 when x x=is-2 when -2. f(-2) = 2(-2) – 3 f(-2) = - 4 – 3 f(-2) = - 7

9. Evaluating a function Tell me what you get x f(x) = 32(2) when x x=is 33. when f(3) = 3 32(2) f(3) = 256

10. Evaluating a function Tell me what you get 2 f(x) = x – 2 x + 3 find whenf(-3) x is -3. 2 (-3) f(-3) = – 2(-3) + 3 f(-3) = 9 + 6 + 3 f(-3) = 18

11. Evaluating a function Tell me what you get f(x) = 3 x + 1 find when f(3) x is 3. f(3) = 3 3 +1 f(3) = 28

Domain and Range • Only list repeats once • Put in order from least to greatest

12. What are the Domain and Range? Domain: {1, 2, 3, 4, 5, 6} Range: {1, 3, 6, 10, 15, 21}

13. What are the Domain and Range? Domain: {0, 1, 2, 3, 4} Range: {1, 2, 4, 8, 16}

14. What are the Domain and Range? Domain: All Reals Range: All Reals

15. What are the Domain and Range? Domain: x ≥ -1 Range: All Reals Is Negative -2 in the domain of this function?