This week in Math 10 we learned ore about linear equations and graphing. Something that I learned was about functions and how to identify when something is a function and when it is a relation. I also learned about function notations.
In a relation the input (x) can have more than one output (y) however, in a function this is not the case.
Function:
- A function is a ‘special’ type of relation
- A function is used to describe when the input (x) has ONLY ONE output (y)
Example:
Function
Relation
Function Notation
I also learned that function notation is used in place of mapping notation since they describe functions.
Mapping notation: f: x -> 2x + 3
Function Notation: f(x) = 2x + 3, in this equation f stands for the name, (x) is the input and, 2x + 3 is the output. f(x) is read as ‘f of x’. It is also important to know that the equation is not saying to multiply f by that of x.
The f(x) notation is another way of stating the value of y in a function, y = f(x)
Equivalent Notations:
- y = 2x + 3
- f (x) = 2x + 3
- x —> 2x + 3
Example:
How to solve:
- First, you need to substitute all the x’s in the equation with 4 since x = 4. When substituting the x’s with their values make sure to add brackets around them.
- Next, (apply B.E.D.M.A.S) multiply the 3 by the 4
- You should then subtract 5 from 12 to get the output
- The answer can also be written as an ordered pair since you know both the input and output, (4,7)