When data is PROPORTIONAL it:
-Has to start at the Origin (0,0). Y-Intercept is 0.
-Has a constant rate of change (m=y/x)
-Has an equation in the form of y=mx
When data is NON-PROPORTIONAL it is missing one of the following:
-Does not start at the Origin (0,0). Y-Intercept is not 0.
-Does not have a constant rate of change (m=y/x)
-Equation is in the form of y=mx+b
A Function is Special
A function is a type of equation.
A function has special rules it must follow:
In a function there can ONLY be ONE output(y) for every input (x).
Just like I stated before, a Function is Special! 🙂
- It must work for every possible input value
- And it has only one relationship for each input value
THIS IS A FUNCTION! THIS IS NOT A FUNCTION!
***Think of the birthday example. Each person can only have 1 birthday, other people might have the same birthday as you but you have only 1. You are like the x (input) value and your birthday the y (output) value.***
Example: y = x²
Could also be written as a table:
It is a function, because:
- Every element in X is related to Y
- No element in X has two or more relationships
- The X values DO NOT repeat
So it follows the rules.
(Notice how both 4 and -4 relate to 16, which is allowed since 4 and -4 are two different numbers.)
Example: This relationship is not a function:
NOT A FUNCTION
This is not a function, for these reasons:
- Value “3” in X has no Y
- Value “4” in X has no Y
- Value “5” is related to more than one value in Y
- REMEMBER THE X VALUE CANNOT REPEAT
Find more information about functions here.