Functions

Functions are a special type of relation. Functions are a type of relation were the x coordinate can only have one corresponding y coordinate. Example: {(-2,9)(-2,8)} this is not a function because the -2 has two y values. All functions are relations, but not all relations are functions. Relations are like friendships because you can have multiple friendships. Functions are like marriages because you can only legally have one.

On a graph you can tell if it’s a function if no parts of the graph share an x coordinate. Most of the time a straight line would be a function except for when the line is vertical. You can test if a graph is a function by moving a vertical line on the graph. If the line doesn’t intercept two parts of the values at the same time then it’s a function.

In equation form if an equation has a degree of 1 then almost always a function. (Linear = a straight line). Example: x= -4 is not a function, but y = 4x + 1 is a function.

Function Notation

f(x) = 3x+1
In this equation the f represents the name of the function, this helps you distinguish the functions from each other. The left of the equation is the input and the right of the equation is the output. If the equal sign is an arrow it tells you how to get the input, but this is mapping notation.
Example: f(4). This tells you what the x in the equation is going to be and which equation to use.
f(4) = 3(4)+1. Replace the x’s with the number.
f(4) = 12 + 1. Solve
f(4) = 13

If you receive the output then you must use algebra to find the input.
Example:
f(x) = 19. This informs you what equation to use and what the out put is.
3x + 1 = 19. Create the equation.
3x +1 -1 = 19 -1. Solve with algebra.
3x/3 = 18
x = 6