Functions Introduction

Functions Introduction

In this unit, we'll be doing two main things: learning what functions are, and learning how to draw graphs. There will be plenty of plotting...but not much scheming. Sorry.

In order to precisely define a function, we'll do a bit of set theory first, which is something you usually don't get to until college or maybe even grad school. However, we can tell that your brain is about to blossom like a brilliant orchid, and we don't want to see that kind of growth get stunted. Besides, once it's finished fully blossoming, we can then pick your brain.

We'll also learn what relations are, in a sense that has nothing to do with your aunts and uncles. You won't be running into any of these at your family reunion, unless some of your relatives are real algebra-hounds.

We'll draw lots and lots of graphs, also known as "pretty pictures that can make your life easier." Be careful, though, since this can also refer to the diagrams included in the instructions on how to assemble a desk from Ikea.

We'll see how to go from equations to graphs and from graphs back to equations. That's right, we're going to buy you a round-trip ticket. We'll spend a while looking at linear equations, which are equations that produce graphs of straight lines. (See the word "line" in the word "linear?")

Finally, we'll look at some types of equations that aren't linear and see what kinds of pictures we get out of those. We're hoping hearts and rainbows, but we're not counting our chickens.

Functions Resources

Websites

PurpleMath: Functions Versus Relations
It isn't quite Alien vs. Predator. They're not pitting functions and relations against each other in a vicious cage match. Instead, this is a good place to go if you need some help understanding the distinctions between functions, relations, and sets. Are you ready to rumble?

Hotmath: Graphing Functions and Relations
To work out your newly developed graphing muscles, take a shot at these practice problems and see how you do. You can hit "View Lesson" for some pointers. Don't hit it too hard, though. It would be nice if your keyboard lasted you a couple of years.

Algebra-class.com: Using a Table of Values to Graph Linear Equations
Tables come in handy, and not just for holding up your dinner. Take a gander at this refresher on using a table of values. By the time you're done, you won't look anywhere near as confused as the poor girl pictured on the site's header.

Video

5min.com: Understanding Graphing Functions
For an in-depth, easy-to-follow explanation of how to graph functions, and what all those numbers, points, and lines really mean, check out this helpful vid. Make sure you free up some time first; it's over half an hour long. Halfway through there's a ten-minute intermission, during which you can go to the bathroom or grab a bucket of popcorn from the concession stand.

Slope-Intercept Rap
Lamar Queen, an 8th grade math teacher, likes to teach his students through the use of rap music—songs he has written specifically to communicate a variety of algebra concepts. We never knew slope could be so dope.

YourTeacher.com: Point Slope Form
Once you've got slope-intercept form down pat, it's time to tackle point-slope form. Here is a helpful example showing you how to convert a linear equation to standard form. If you can figure out a way to also convert it to raw energy, the federal government may have a job for you.

Games and Tools

Quia: Domain and Range
Test your knowledge in this Jeopardy-style game where you can try your luck with Ordered Pair problems, Mapping problems, and Solving problems. Score enough points and you could beat…no one. Because you're playing alone. You can still do a victory lap, though.

Math is Fun: Function Grapher and Calculator
Plug in any function, hit "Plot," and you'll see the corresponding graph of that function appear before your very eyes. Hopefully not right in front of your very eyes, because that means you're sitting too close to the computer monitor.

CRCTLessons: Slope-Intercept Game
Practice your slope-intercept skills as well as your hoop skillz at the same time. You only get to take a shot at the basket when you answer correctly though, so no warm-up shots until you start nailing these problems. Bonus points if you hit one from outside the arc.

Purpose Games: Quadratic Functions
See if you can match up each graphed parabola with the quadratic function given. Get them all right and do so quickly, and you may make the high scorer's list. If you don't make the list, don't sweat it. Those guys at the top are probably cheating anyway. Like anybody's fingers are that fast.