Whenever we can classify a function as one of the familiar types such as quadratic or trigonometric, we know it will have certain wellknown properties. For example, a trigonometric function will be periodic. As you learn to use the vocabulary of functions more and more precisely, it will be easier for you to read mathematics with genuine understanding. When you are first presented with any formula, you should try to establish what type of a function it describes. This may require you to rewrite the function in order to convert it into a standard form.
The form of a linear function is easily recognizable:
A function is quadratic if it can be put in the form
Note also that a must be nonzero  if a is zero,
we just have a line.
A function is cubic if it can be put in the form
Note again that a must be nonzero.
A polynomial function can be written in the form
where n is a nonnegative integer (note that this
means that all of the exponents are integers), and all of the
coefficients are constants. Of course, linear, quadratic and cubic
functions are all also polynomials.
All of the four preceding types (linear, quadratic, cubic, polynomial)
are special cases of the broader category called rational
functions, which is made up of all quotients of polynomials. The
rational functions can be written in the form
A power function is a function formed by raising a variable to a
constant power and then multiplying by a constant  which may be
one. Power functions can therefore be written in the form
Note that a, and r are real numbers.
These functions are formed in a different way from power functions.
An exponential function is a constant raised to a variable
power (and then multiplying by a constant). An exponential
function can therefore be written in the form
Note that b must be positive.
These are easy to recognize because the name of the function is always
included in the expression. The definitions are
the inverse of the exponential


the inverse of the exponential

Remember that an expression like ln(3) is a constant!
Trigonometric functions are designated by name in mathematical
writing. The definitions, which refer to the unit circle, are
Be sure you've gone through each step in the examples above before doing these. Once you've worked them until you're sure that you understand them, go on to the next section. There are more problems of this type in the section test at the end of the section.