# Functions

Welcome to the second week’s session for MATH 107! This week, take a look at functions and we look at basic graphing. This is an extension of the material we were working with last week So let’s get started. We’ll have some more interactive materials, this week, too.

## Linear Functions

Functions are the idea that we can take a set of things and for each member of that set, there is a member of another set which it corresponds to. We call this a mapping. In these examples, the two sets of things are both the sets of numbers. So a function takes a number, which we will call \$x\$ and shows how it corresponds to another number, which we will call $y$. We often use the notation $f(x)$ to represent a function. We might also use the notation $y =$ to show the mapping between $x$ and $y$. Watch these for how to recognize linear functions.

Check this out to interactive to test a linear function.

[WolframCDF source=”http://demonstrations.wolfram.com/TwoPointsDetermineALine/TwoPointsDetermineALine.cdf” width=”900″ height=”650″]

And try this interactive to try putting different slopes in points to make lines.

[WolframCDF source=”http://demonstrations.wolfram.com/SlopeAndEquationsOfLinesThroughPoints/SlopeAndEquationsOfLinesThroughPoints.cdf” width=”800″ height=”625″]

This final video shows how to put parallel and perpendicular lines relate to the original line.