Posted By StudyGate
Graphing Functions: A How to Guide for Graph Calculator

Math brings out the artist in you!

While the industrious student can simply whip out a graph calculator to draw up graphing functions, figuring out functions the old-fashioned way can be pretty keen. With nothing but a pencil and a piece of paper divided into little squares, we can create lines and make ‘em dance to the curve of a slope intercept form. Oh yeah, remember that you can hire an online math tutor from Studygate!

We all knew math was a cute little number, but here is where we prove it!

Let’s take a simple equation:

y = mx + b

This is a pretty basic format for graphing. We have a Y axis that has a direct relationship with the X axis. The ratio between Y and X is determined by M.

Let’s throw in some numbers and see where they land:

y = 2x + 6

This is as easy as it gets. Let’s whip up a graph:

Let’s start easy, with x = 0.

So we know that when X is at 0, Y is 6. The “2” is the ratio between X and Y. If X was 1, then simply multiply X x 2 + 6 = 8.

We can create a quick chart between X and Y. Don’t forget that we can go into negative values for X and Y s as well!

 X Y -4 -2 -3 0 -2 2 -1 4 0 6 1 8 2 10 3 12 4 14 5 16 6 18 7 20

Then, plot the points and connect to form a line!

Pretty neat, huh?

****QUICK TIP: go back to the equation

We can break M down to represent the change over Y over the change over X. If it were a fraction, it would look like this: change over Y ÷ change over X

Since 2 is basically 2÷1, we can simply say that for every change in X, we move Y up 2 spaces! Look at the chart and do the math. See how it works?

What is M was a fraction?It still works out:

This means that for every X value we have, Y goes up by . The chart would look like:

 X Y -4 -1 -3 -.25 -2 .5 -1 1.25 0 2 1 2.75 2 3.5 3 4.25 4 5 5 5.75 6 6.5 7 7.25

Graphs with fraction M look less steep than graphs where M is a whole number.

But where does this get us with graphing functions?

It’s really easy: it’s basically the same thing!

ƒ(x) = x2 + 2

In this case, Y = F(x). Since the equation is squared, there will be some curves as the Y intercept changes from positive to negative. But the procedure is the same.

So let’s throw some X values in and see what we get! You can also contact an online math tutor to complete this step.

 X Y -5 23 -4 18 -3 11 -2 6 -1 3 0 2 1 3 2 6 3 11 4 18 5 23

As you can see, we have a curve!

Imagine the possibilities: with numbers, you can draw anything!

For more math tips our guide to solving the quadratic formula will help.