INTRODUCTION TO FUNCTIONS

A function is a rule that takes an input, does something to it, and gives an output.
Each input has exactly one output.

It is often helpful to think of a function as a box.
You drop an input in the top, something happens to the input inside the box,
and the output drops out the bottom.

The box (the function) can be labeled with what it does.
For example, if the box is labeled ‘add 2’,
then when the number $\,3\,$ is dropped in the top,
the number $\,3+2 = 5\,$ comes out the bottom:

[beautiful math coming... please be patient] $\displaystyle \overset{\text{input}}{\overbrace{\ \ 3\ \ }} \overset{\text{the function adds 2}} { \overset{\text{to the input}}{\overbrace{\strut\ +\ \ 2\ }} } \overset{\text{and produces }}{\overbrace{\strut\ \ =\ \ }} \overset{\text{the output}}{\overbrace{\strut\ \ 5\ \ }} $

EXAMPLES:
Question: Consider the ‘add $\,2\,$’ function.
If $\,3\,$ is the input, then what is the output?
Answer: $3 + 2 = 5$
Question: Consider the ‘add $\,2\,$’ function.
If [beautiful math coming... please be patient] $\,x\,$ is the input, then what is the output?
Answer: [beautiful math coming... please be patient] $x + 2$
Question: Consider the ‘add $\,2\,$’ function.
If [beautiful math coming... please be patient] $\,x + 3\,$ is the input, then what is the output?
Answer: [beautiful math coming... please be patient] $(x + 3) + 2 = x + 5$
Question: Consider the ‘multiply by $\,2\,$’ function.
If $\,x + 5\,$ is the input, then what is the output?
Answer: [beautiful math coming... please be patient] $2(x + 5) = 2x + 10$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Introduction to Function Notation

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
(MAX is 24; there are 24 different problem types.)