1. Functions and Graphs Introduction

2. Use the “Functions and Graphs Vocab Guided Notes Worksheet” to take notes as we go
Basic definitions are written for you
Add in additional ideas and tips
Draw in examples
Highlight or underline what helps you

3. Vocabulary
Relation
Relation – Is the mapping between a set of input values (x) and output values (y). They show a relationship between sets of information, can be represented in ordered pairs, table, graph, or mapping
Any set of ordered pairs can be used in a relation.
No specific rule required
Examples:
(1, 40), (1, 50), (2, 65), (2, 75), (3, 80)…
{(A, Frankie), (C, Denise), (B, Brady), (A, Julietta), (D, Bob), (B, Evelyn)}
(0,0), (1, 1), (1, -1), (2, 1.414…), (2, …)…

4. Vocabulary
Function
Function: a relation between a given set of elements for which each input value (x) there exists exactly one output value (y).
A function is a more specific type of relation. It has to follow certain ‘rules’
*no repeat x values allowed with different y outputs
One x-value cannot have more than one y-value. (6, 8) and (6, 20)
NOT a function because the input of 6 has two different outputs
(can’t have repeat xs with different ys)
One y-value can have more than x-value. (7, 4) and (9, 4)
YES it is a function because the each input has only one output
(it’s ok to have repeated y values)
Examples:
(1, 40), (2, 65), (3, 80), (5, 90), (6, 80), (7, 85)
(0,0), (1, 1), (2, 1.414…), (3, …), (4, 2)…

5. How to determine if a relation is a function:
Analyze the x-values given in ordered pairs or in a table.
If an x repeats with a different y-value, then it is NOT a function.
Practice: State if the relation is a function
H = {(2, 5), (3, 9), (-4, 10), (6, -6), (-7, 5)}
M = {(3, 7), (-8, 2), (-1, 0), (3, 8), (2, 6)} 3. 4.
Function
Not a function
Not a function
Function
The input of 3 has two different outputs
The input of 4 has two different outputs

6. How to determine if a graph is a function:
Vertical Line Test = A visual method used to determine whether a relation represented as a graph is a function
If you draw a vertical line anywhere on the graph and it goes through only one point = FUNCTION
If you draw a vertical line anywhere on the graph and it goes through more than one point = NOT a Function.
This tells you if an input has only one or more than one corresponding y output
Practice: Is this graph a function? x y x y
Yes, function
Not a function
Not a function
Yes, function

7. Vocabulary Function Notation
Is a way to represent functions algebraically that makes it more efficient to recognize the independent and dependent variables.
a way of writing a function.
The most popular way to write a function is f(x).
This is read “f of x”
f(x)= is same as saying y=
This tells you that x is the input/independent variable
(This is NOT multiplying f times x.)
Example:
f(x) = 2x + 4
It is very similar to saying y = 2x + 4 as we did in pre-algebra
x is still input
output
input
f(x) is the output instead of y
f(3) = 2(3) + 4 Plug the x input 3 into the ‘rule’ 2x+4
f(3) = 10 means with input 3, the function’s output is 10

8. How to use function notation f(x)…
f(x) = 2x + 7, find f(5).
This is asking what is the value of the function when the input/independent variable is 5
Substitute 5 in where you see x and evaluate.
f(5) = 2(5) + 7
f(5) = 17 The answer is 17.
f(x) = -3x2 – x – 4, find f(2)
This means to substitute 2 in where you see x.
f(2) = -3(2)2 – 2 – 4
f(2) = -18

9. General Graph Vocab

10. General Graph Vocab