Graphing Functions

Tutoring on Graphing Functions

Learning Objectives:

Understand to Graph a Function.


Graphing Functions 

A function (a set of ordered pair) is a special relationship where each input has a single output. While  graphing, if we're not sure what the function looks like we can always go back to making a table of values and notice how all the functions will be given using function notation, as well as replacing (f of x) with y. We graph functions in exactly the same way that we graph equations.  If we know ahead of time what the function is a graph of we can use that information to help us with the graph and if we don’t know what the function is ahead of time then all we need to do is plug in some x’s compute the value of the function (which is really a y value) and then plot the points. In order to graph a linear equation we work in 3 steps: First we solve the equation for y.

Second we make a table for our x- and y-values. From the x values we determine our y-values.

Last we graph our matching x- and y-values and draw a line. Therefore the graph of a function f  is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x).


Hook Questions


1.    How do you graph a quadratic equation?

2.    How do you graph a rational function?


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