Types of functions for Algebra


There are many types of functions in mathematics. The first we will discuss is a linear function. The first thing that you should notice is that it is a straight line, thus the name LINEar. This means that for every change in the value of x there will be a specific amount of change in y.

The second type of function that will be discussed is the quadratic functions. The first thing you should notice is that this function is not a straight line, but instead is a curve. In this particular case, you will also notice symmetry with the y-axis, that is, for +/- of the same x-value, you would get exactly the same y-value.

X-value -4 -3 -2 -1 0 1 2 3 4
Y-value 2 -1.5 -4 -5.5 -6 -5.5 -4 -1.5 2

The next function we will look at is the cubic functions. These functions are similar to a linear function except that there is two little 'mini-parabolas' near the origin. In this case you will notice again the symmetry with respect to the y-axis, such that the y-values are symmetric with the line at y = -2, as well as, mirror images that have been 'double flipped'.

X-value -3 -2 -1 0 1 2 3
Y-value -29 -10 -3 -2 -1 6 25
Distance from y = -2 27 -8 1 -0 1 8 27

The next function to be discussed will be the quartic equations In this particular case, the equation is symmetric with respect to the y-axis as shown in the graph and the table below.The function is very much like a quadratic, in that is is parabolic in shape, but also has the little reverse parabolas like the cubic functions.

X-value -4 -3 -2 -1 0 1 2 3 4
Y-value 67.4 11.4 -4.6 -4.6 -3 -4.6 -4.6 11.4 67.4

The next function family this page will discuss are the trigonometric functions sine, cosine, and tangent. All of these functions are of a periodic nature, that is, they repeat at a specific interval. You will notice that sine and cosine are almost identical, except that cosine starts at the top of the wave and sine starts in the middle in the wave. Tangent just does it own thing.

Well that's all for this lesson. Talk to you later.....