8th Grade Algebra Review - Graphs & Functions  

A function is a relationship between input and output. The output depends on the input and there is exactly one output for each input.

A coordinate system is formed by the intersection of two number lines - the horizontal axis called the x-axis, and the vertical axis called the y-axis.

In a function, each input and its corresponding output is represented on a graph using ordered pairs. An ordered pair is a set of numbers; one is the x-coordinate of the input value on the graph, and the other is the y-coordinate of the output value.

It is expressed a (x,y).

In a function, if one variable can be dependent on another variable. For example, if distance traveled equals 60 times the number of hours spent driving at 60 mph, then we can represent this with the function

 d = 60 t  

d is the dependent variable and t is the independent variable.

d depends on the value of t. If we graph this function, d, the dependent variable, would be plotted on the y-axis; and t, the independent variable, would be plotted on the x-axis.

On a graph, the set of ordered pairs is called a relation. The set of the first numbers, (the x-axis values), is the domain. The domain contains all values of the independent variable.

The set of the second numbers, (the y-axis values), is the range of the relation. The range contains all values of the dependent variable.