What is functional notation?

Functional notation is a way of writing a function. Traditionally ???f(x)??? is how a function is written, but really any variables may be used.

The function name is the ???f??? or the variable outside of parentheses and the variable used for input is ???x??? or the variable that’s inside the parentheses.

In order to find the output of a specific input we can replace the ???x??? with any number we want. If we wanted to find the output when ???x=2???, we’d write ???f(2)??? and then plug in ???2??? for every ???x??? in the equation.

How to evaluate functions that are written with functional notation

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Let’s work through a couple of examples where we evaluate the function at a particular value

Example

If ???f(x)=10-2x???, find ???f(-6)???.

Notice that ???-6??? is where the ???x??? is in ???f(x)???, which means that we’ll substitute or plug ???-6??? in for ???x??? in our function. Remember to use parentheses when plugging in numbers.

???f(-6)=10-2(-6)???

Now we’ll simplify the right side following the order of operations.

???f(-6)=10+12???

???f(-6)=22???

Let’s try another example of functional notation.

Example

If ???f(x)=x^2-7x+12???, find ???f(4)???.

Plug ???4??? in for ???x??? in the function.

???f(4)=(4)^2-7(4)+12???

Now simplify following the order of operations.

???f(4)=16-28+12???

???f(4)=-12+12???

???f(4)=0???

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