Functions, Graphs, and Limits Topics

Functions are usually written something like this: y = f(x).x is called the independent variable, while y is called the dependent variable. The independ...

Some things are untouchable. The Mona Lisa, magma...asymptotes? An asymptote is a line to which a function gets infinitely close. There are several different types of asymptotes, it will be our ple...

Vertical asymptotes occur where a function f(x) has a limit of infinity - that is, at values of a for whichWe can also take limits as x goes to ∞ or -∞, writtenThese limits look at where the fu...

When we find the limit of a function f(x) as x goes to infinity, we're answering the question "What value is f(x) approaching as x gets bigger and bigger and bigger...?''A rockin' example of this i...

We've talked about vertical asymptotes where y runs off forever, but whoever said x can't ride off into the sunset (or the negative sunset), too? In this section we'll talk about other types of asy...

We now have enough tools to draw some complicated functions from scratch. Now we know how graphing calculators do it, and why they require the energy of four triple-A's.When drawing a rational func...

Power the race horse, Polly the parrot, and Log the log walk...or roll...into a bar. After a couple root beers, Log challenges the others to a race on a horse track. Who will we bet on? Power, of c...

Why can't limits all get along? Ignoring them is not the answer. Sometimes we need to show them who's boss by separating them, calming them down, and then bringing them back together again.There ar...

Sometime measurements and results aren't perfect. This is true in science, engineering and life. How close to 16.9 fluid ounces of Mathlete-ade can a plastic bottle hold in order to allow 16.9 f...