Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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Throughout mathematics, we find function notation. **Function notation** is a way to write functions that is easy to read and understand. Functions have dependent and independent variables, and when we use function notation the independent variable is commonly x, and the dependent variable is F(x). In order to write a relation or equation using function notation, we first determine whether the relation is a function.

Function notation is a different way of writing a relationship, okay. So for this particular example we're going to take you back to something that you already know, okay? y=4x-2 it's the equation of a line and we're asked to find y when x=1. We just plug in 1, solve it out. So y=4x1-2, 4 times one is 4, minus 2 is equal to 2. So when x is 1, y is 2, pretty straight forward.

What function notation is is just a different way of writing the same exact problem, okay? And what function notation is, I'm actually going to just [IB] is, f of x, this is said, f of x. You're basically saying, y is a function of x, y is dependent on whatever x is, okay? So here, you're just replacing that with the dependency factor. And so this is exactly the same as this. So instead of saying find y when x=1, what we can actually write is just f of 1, okay? So it's just saying find y when x=1, you will do exact same thing, 4 times 1 minus 2 is equal to 2, okay.

Check for this is, these two statements are exactly the same. What people want to do is say, okay, multiply this by x, something like that. There really is no need for that, all you really need to remember is f of x is just equal to y value. And whenever they say find something, you plug this value in for x.