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Function Notation  Concept
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
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.
One thing you'll find in your math classes
is that there's lots of different ways
to write the same thing.
And although sometimes it can be confusing,
it's actually pretty cool, because
it helps you keep track of what variable
or what letter is affecting which
one.
Like, for example, most of the time
X is the independent variable.
And Y is the dependent variable.
What that means is that your Y value
depends on whatever X was.
X can usually change on its own.
And whatever X does affects what Y is.
That's why we call Y the dependent variable.
So one way this is written is it's kind of
different from what you've seen before.
What you've seen before is probably
something like this.
Y equals 3X plus 2. A new way to write
that is using what's called function
notation.
Instead of Y, I'm going to say
F of X.
What that means is the function that's
using X is equal to 3X plus 2. It's
the same thing written
in two different ways.
I think it's kind of neat when we get into
doing some more problems with numbers
is that I can stick a number in there
for X and I can show what number
that is here as well.
You can kind of tell what X number you're
plugging in, the independent variable,
to get your Y value output variable.
One last thing to keep in mind when you're
working with functions and function
notation is the ideas
of domain and range.
Domain is the set of all X values
or the independent variables.
Range is the set of Y values
or the dependent variables.
Which means that your domain
changes on its own.
It's independent.
Your range is dependent
on that domain stuff.
It's a lot to keep track in your head.
As you can tell my head is kind
of struggling with it, too.
But you can see as we get going with some
problems you can keep it all straight
and do a good job with
notation function.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
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Sample Problems (7)
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Function Notation
Problem 1 11,587 viewsRudy earns $25 per hour in his summer job.
a) Write a function f(x) to describe his earnings.b) Evaluate your function when x = 5 hours.c) How many hours did he work if he earned $150? 
Function Notation
Problem 2 7,205 viewsg(x) = 4x − 3
a) Find g(3)b) Find x when g(x) = 29 
Function Notation
Problem 3 6,030 viewsMultiple Choice: Which function best models the data?
x 0 1 2 3 f(x) 1 1 3 5 A. f(x) = 1x + 2B. f(x) = 2x + 3C. f(x) = 2x − 1D. f(x) = 2x 
Function Notation
Problem 4 734 views 
Function Notation
Problem 5 479 views 
Function Notation
Problem 6 581 views 
Function Notation
Problem 7 460 views
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