Function Notation

When we write a function in the form $y\left(x\right)\:$or $f\left(x\right)\:$we say "y or x" or "f of x", and this notation means that x is the dependent variable, and either y or f is the dependent variable.    The video below shows several examples of how to evaluate functions using function notation. 

Since $f\left(x\right)\:$replaces the independent variable y in an equation. If we want to put an equation into function notation, we first need to solve for y and then replace y with $f\left(x\right).$

Example

Assume that y is a function f of x. Rewrite the equation $2x-3y=7$ using function notation. Then find $f\left(-2\right)\:$and $f\left(p\right).$

Solution

First we need to solve $2x-3y=7$ for y.

$2x-3y=7$

Subtracting 2x from both sides gives us

$-3y=-2x+7$

Dividing both sides by -3  gives us

$y=\frac{2}{3}x-\frac{7}{3}$

Now we can replace the y with f(x) to write the equation in function notation.

$f\left(x\right)=\frac{2}{3}x-\frac{7}{3}$

Now we are ready to evaluate

 $f\left(-2\right)\:$and $f\left(p\right).$

$f\left(-2\right)=\frac{2}{3}\left(-2\right)-\frac{7}{3}=\frac{-4}{3}-\frac{7}{3}=\frac{-11}{3}\:or-3\frac{2}{3}\:$

$f\left(p\right)=\frac{2}{3}p-\frac{7}{3}$