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### Functions

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Date: Sat, 12 Nov 1994 22:20:32 -0500 (EST)
From: Anonymous
Subject: functions

Hi, I'm a first year algebra student having difficulty learning about
functions.  Exactly how do functions work?  Currently, I'm on
exponential functions and going to be hitting logrithms.  HELP!!!
I got lost on functions a couple chapters back, but would like to catch up.

Thanks.   markm@epix.net
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Date: Sun, 13 Nov 1994 10:18:23 -0500 (EST)
From: Dr. Sydney
Subject: Re: functions

Dear Mark,

Thanks for writing Dr. Math!  You know, I had similar problems when
I was learning about functions -- it took a little while for me to figure
out what they were all about.  I'll try to help you understand better.  For
now, you're probably only dealing with functions of one variable, so I'll
focus on that.  You know what an equation with two variables is, right?
You can think of a function as being very similar to an equation with two
variables, where you solve for one of the variables.  For instance,
the equation:

y + x = 28

can be made into a function by solving for x or y (let's
choose y):

y = 28 - x

We can write this as a function of x:

f(x)= 28 - x

Another way to think about functions is to imagine them as a formula
of sorts for changing the number you start with (the "x" ) into a new number
(f(x))

So, with the function

f(x) = 28 - x

the function takes the additive inverse of a number, x, and adds 28 for all x.

On to harder examples, such as the exponential and logarithmic functions:

x
f(x) = e

e is a special constant, not a variable.  So this function takes any number
x and raises e to that power.  Do you know what the graph of this function
will look like?  e is a positive number, so will f(x) ever be negative or
0?  These are good questions to ask yourself.

Sometimes it is easier to imagine a function if you plug in a variable for
the "f(x)" term.  So for the exponential function, it might be easier to
think about the equation :

x
y=e

What about the logarithmic function?

f(x) = ln(x)

Again, you might want to think of this as:

y = ln(x)

this relation is the same as:

y
e = x

Does this look familiar?  What is similar between the exponential and
logarithmic functions?  These two functions are called inverses.  Do you
know why?

I hope this helps some.  I think you will gain a better understanding with
time.  If you have any questions about this or anything else, please feel
free to write back.

--Sydney, "dr.function"
```
Associated Topics:
High School Basic Algebra
High School Functions

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