Types of Mathematical Functions

Transcendental Functions

If we cannot express a function algebraically, it is a transcendental function:

• Trigonometric (Circular) Functions are relations expressed as ratios of sides of a right triangle. An example would be: \(f(x)=\sin (x)\)
• Exponential Functions depict situations of growth or decay. An example would be: \(f(x)=e^x\)
• Logarithmic Functions are the inverse of exponential functions. An example would be: \(f(x)=\log (x)\)
• Hyperbolic Functions are functions identical to circular functions but based on the hyperbola. An example would be: \(f(x)=\sinh(x)\)

Other Functions

The types we've discussed above are not the only functions. Other unique relations include absolute, sawtooth, etc. 

We can also combine different types to create a new one. For example, we can combine polynomials with trigonometric functions.

Summary

There are two basic types of functions: algebraic and transcendental. 

An algebraic function is one we can express in terms of algebra terms. Examples include polynomial, rational, and radical functions.

If we cannot express a function algebraically, it is a transcendental function. Examples include trigonometric, exponential, logarithmic, and hyperbolic.