# Functions, Graphs, and Limits

# Functions, Graphs, and Limits Topics

## Functions, Graphs, and Limits explanations, examples, practice problems. Ready? Let’s do this.

#### Limits

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...

#### All About Asymptotes

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...

#### Limits at Infinity

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...

#### Limits of Functions at Infinity

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...

#### Horizontal, Slant, and Curvilinear Asymptotes

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...

#### How to Draw Rational Functions from Scratch

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...

#### Comparing Functions

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...

#### Manipulating Limits

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...

#### In the Real World

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...