# Algebraic Functions

# Basic Understanding of Algebraic Functions

**Algebraic functions**are function that can be defined using algebraic operations.- They involve variables, constants and operations – addition, subtraction, multiplication, division, and exponentiation.
- Examples include polynomial functions, rational functions, exponential functions, and so on.

# Function Notation

- Function notation involves writing functions as
or*f(x)*, where*g(x)*or*f*is the function, and*g*is the input.*x* - In an equation
,*y = f(x)*is the output corresponding to an input*y*.*x*

# Evaluating Functions

**Function evaluation**involves substitifying a specific value for the variable in the function.- If you have a function
, by replacing*f(x)*with a number, you can find the output or the value of the function.*x* - For example, if
, then*f(x) = 2x + 3**.*f(2) = (2*2) + 3 = 7

# Types of Functions

**Linear functions**are functions of the formwhere*f(x) = mx + c*and*m*are constants.*c***Quadratic functions**are functions of the form, where*f(x) = ax^2 + bx + c*,*a*and*b*are constants.*c***Cubic functions**are functions of the form, where*f(x) = ax^3 + bx^2 + cx + d*,*a*,*b*and*c*are constants.*d*- Note that quadratic and cubic functions exhibit more complex behavior than linear functions.

# Inverse Functions

- An
**inverse function**, denoted as, is a function that undoes the operation of the original function.*f^(-1)(x)* - It flips the x and y in a function.
- Note the difference between the inverse function, written as
, and a reciprocal function, sometimes described as*f^(-1)(x)*.*f^-1(x)*

# Understanding Domain and Range

**Domain**refers to the set of all possible input values (x-values) for a function.**Range**refers to the set of all possible output values (y-values) for a function.- Understanding how to calculate the domain and the range is crucial when dealing with different calculus equations involving functions.