Functions are classified by the type of mathematical equation which represents their relationship. Some functions are algebraic. Other functions like f(x) = sin x, deal with angles and are known as trigonometric. Still other functions have logarithmic and exponential relationships and are classified as such.

One method for identifying functions is to look at the difference or the ratio of different values of the dependent variable. For example, if the difference between values of the dependent variable is the same each time we change the independent variable by the same amount, then the function is linear.

Types of Functions

• Algebraic Function: A function defined by an algebraic expression is called an algebraic function.
• Polynomial Function: A function of the form P(x)=amxn+an–1xn–1+⋯+a1x+a0.
• Linear Function:
• Quadratic Function:
• Cubic Function:
• Identity Function:
• Rational Function:
• Trigonometric Function:

Overall, the steps for algebraically finding the range of a function are:

1. Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
2. Find the domain of g(y), and this will be the range of f(x).
3. If you can’t seem to solve for x, then try graphing the function to find the range.

A rational function is one such that f(x)=P(x)Q(x) f ( x ) = P ( x ) Q ( x ) , where Q(x)≠0 Q ( x ) ≠ 0 ; the domain of a rational function can be calculated.

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

A linear function is a function whose graph is a straight line. The line can’t be vertical, since then we wouldn’t have a function, but any other sort of straight line is fine. This graph shows two lines, rather than one straight line. …