Polynomial Functions:
These are functions that have terms which are powers of the variable, multiplied by a real number.
Examples:

f ( x ) = 3 x5 - 7 x + 8

g ( a ) = a2 - 9

You should recognize g ( a ) as the difference of two squares. It can be factored as

g ( a ) = ( a - 3 ) ( a + 3 )

This will be = 0 when a = 3 or a = - 3.

Often polynomial equations are solved using the "Zero Product" rule. If a b = 0, then a = 0 or b = 0.

Problem: x4 + 3 x3 = 10 x2

You can subtract 10 x 2 from both sides to have a polynomial = 0. Then factor.

x 2 ( x + 5 ) ( x - 2 ) = 0

Therefore, x = 0, x = -5, and x = 2 are all solutions to this equation.

If you had any trouble factoring this, you may need to practice factoring skills.
Check out the page on this by Purple Math.

Exponential functions are of the form: f ( x ) = ax

Notice that if x = 0, then f ( 0 ) = 1.

For negative exponents you will have values less than 1.
For positive exponents the values are greater than 1 and increase very rapidly.
Here is an example of an exponential function:

Exponential_Function.png
f(x) = 3^x


If we use -x in the exponent, we will get a decreasing function.

Exponential_Function_decreasing.png
f(x) = 3^(-x)