# Linear, Quadratic, and Exponential Models

Functions are a type of mathematical relationship between inputs and outputs. In this guide, you will learn more about types of functions.

## A step-by-step guide tolinear, quadratic, and exponential models

Functions are a type of mathematical relationship between inputs and outputs. The linear, quadratic, and exponential functions are the $$3$$ main types of functions.

### Linear function:

A linear function is a type of function whose highest exponent is $$1$$. The standard form of this function is $$y=mx + b$$. The graph of the linear function shows a straight line in the coordinate plane.

A quadratic function is a polynomial function with one or more variables, where the highest power of the variable is two. Since the highest degree in a quadratic function is of the second degree, therefore it is also called the polynomial of degree $$2$$.

The quadratic function when graphed makes parabolas. The standard form of a quadratic function is $$f(x) = ax^2+bx + c$$, where $$a, b,$$ and $$c$$ are real numbers with $$a≠0$$.

### Exponential function:

An exponential function is a function of form $$f(x)= a^x$$, where $$x$$ is a variable and $$a$$ is a constant, which is called the base of the function and must be greater than $$0$$. Exponential function graphs have curves. This curve can be vertical at first and then grow horizontally, or it can be horizontal at first and then become more vertical.

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