How to graph a linear function or linear equation

y= mx + b

The y is your output (dependent variable, range)
The x is your input (independent variable, domain)
You use these to plug in points to test if points are solutions of a line
The m is your slope which has to be written as a fraction to plot points using rise over run
The b is your y intercept

Negative Slope

Positive Slope

Relations and Functions

Relations are a set of points either given in a 

list, table, mapping, or graph

Here are two examples of relations given in a list, graph, and a mapping. In a mapping make sure you only write numbers once if they repeat!

Important Vocab!!!!

Input- x values, independent variable, domain

Output- y values, dependent variable, range

Functions- 

Fancy definition- functions are relations where there is only one domain for every range (only one input for every output)

Basic definition- for a relation to be a function the domain (x-values) CANNOT repeat

Ways to test a if a relation is a function

Given a table, list, or mapping: check and make sure the x values don't repeat- if they do... it's a NOT function!

Given a graph: use the vertical line test!What is the vertical line test? If you draw a vertical line on the graph- that vertical line can only touch one point at a time or it is NOT a function

See below for examples of testing if a function on a graph using the vertical line test. The yellow lines are an example of the vertical line test. 

More can be found in 4-5 and 4-6 in your textbook. 

Different types of Graphs- Linear and Nonlinear

Sets- Unions, Intersections, Complements of Sets

Percent of Change

Solving Compound Inequalities, Set Builder Notation, and Interval Notation