1. Functions!

2. What is a relation? (purple)
Any set of ordered pairs:
In a list
In a table
In a mapping diagram
On a graph

3. What is a function? (purple)
A one-to-one rule that gives one output for any input. ** x CANNOT repeat**

4. Ordered pairs (pink)
We always write ORDERED PAIRS in curly braces with commas in between the ordered pairs. {(1,5), (-2,7), (4,3), (0,0) (-2,-3)} There are repeating x-values, so the example is NOT a function.

5. Input/output table (pink)
The input (domain) is always “x”. They output (range) is always “y”.
In a VERTICAL table, “x” always goes on the left side, & “y” on the right.
In a HORIZONTAL table, “x” always goes on top, & “y” on the bottom. x y 2 3 -4 1 5 -2 x 1 7 3 y -4 9 -2 8
The first table is a function because none of the x-values repeat. The second table is NOT a function because there are repeating x-values (the 1’s).

6. Coordinate plane (Pink)
The X-COORDINATE tells us to move left/right. The Y-COORDINATE tells us to move up/down.
To check if a graph is a function, we use the VERTICAL LINE TEST. If you ran a vertical line over a graph and it ever touched more than one point, the graph is NOT a function.

7. Mapping diagram (pink)
In the LEFT box/oval, write all input values (“x”). DO NOT REPEAT ANY!
In the RIGHT box/oval, write all output values (“y”). DO NOT REPEAT ANY!
Draw an arrow from each INPUT value to its OUTPUT value.
Input
Output
The mapping to the left is NOT a function because there are multiple arrows coming from one input value. A function should have one arrow from each input value. 1 2 3 -2 1 7

8. Domain and Range (purple)
Collection of inputs
X-values
Independent variables
Range
Collection of outputs
Y-values
Dependent variables

9. Independent and dependent Variables (Blue)
Changing the independent variable
Dependent variable
Causes change in the
X is always the independent variable.
Y is always the dependent variable.

10. Function machine (purple)
y=2x+3 x y 4 11 -1 1 2 7 21 3 5 9 13
2(4)+3

11. Function machines & function notation (yellow)
A function can be though of as a machine that assigns the output to every input.
f(x)=3x+4
Name of the function
Tells what number to plug into the function
f(x) means the output of the function f when the input is x. We often refer to this as y.
THE FUNCTION!!

13. Let f(x)=x2+3 and g(x)=x+1
f(3) g(3) f(-2) g(0) f(2)+g(1)
g(-1)+f(1) f(g(2)) g(f(0)) f(y) g(w)