What is a Function?
A function is a relationship where each input value has only one output value. For example:
f(x) = x2 is a function because no matter what the value of x is, x2 has only one value f(x):
If f(x)2 = x, then is NOT a function because every x value has TWO values for f(x)
Instead of using lengthy verbal descriptions like you did in the intro activity, you can use an equation to describe what a function will do. Function notation is a way to express how the function transforms the input into the output, such as: f(x) = x + 5. This means that this function named “f” operates on the variable “x” and it adds 5 to it. If you put x ‘into’ this function, f(x) tells you what comes ‘out.’ A few things to remember about function notation:
The input can be represented by any variable, though ‘x’ is used most often unless another variable makes more sense for a particular problem.
The output is represented as f(x) which reads “the function ‘f’ of ‘x’ “ or just “f of x” for short.
The most common letter to define a function is ‘f’ though any could be used (e.g. g(x), h(x), m(x) )
Example 1
Johnny triples his money by investing, and then pays $2 in capital gains taxes when he sells those investments. Write this using function notation where x is the amount of money Johnny starts with.
1
Represent the steps of the function:
Write the steps in the order they happen in the function using an input variable
1) Start with x
2) Multiply x by 3
3) Subtract 2 from the result
2
Write an equation for the function:
Using parentheses initially may help keep track of the order of operations
f(x) = (x * 3) - 2
f(x) = 3x - 2