# Functions

# Functions Examples

#### Relations

An ordered pair is a pair of things, but in this case we actually care which is first and which is second. You know what they say about second: first loser.To write an ordered pair, we write down t...

#### Functions

A function is a special kind of relation where each thing in the domain may be paired with only one thing in the range. These guys are all about monogamous relationships.
Sample ProblemHere's...

#### Graphing an Ordered Pair

We already have a place set up and waiting for us to graph all over it, so let's take advantage. We'll start by graphing the ordered pair (2, 3). In order to do so, we start at the origin, go 2 to...

#### Graphing Relations

Graphing a finite relation just means graphing a bunch of ordered pairs at once. Don't freak out. You can still draw the dots one at a time. It would be amazing if you could draw them all in one fe...

#### Graphing Functions

Remember: a function is a relation where each thing in the domain is matched with only one thing in the range. Another way to say this is that each x value gets matched with only one y value. We ca...

#### Linear Functions and Equations

A linear function is a function whose graph is a straight line. The line can't be vertical, since then we wouldn't have a function, but any other sort of straight line is fine. Now, are you ready t...

#### Standard Form

A linear equation in standard form is an equation that looks likeax + by = cwhere a, b, and c are real numbers and a and b aren't both zero. c can be zero if it wants. It's the favorite chi...

#### Slope-Intercept Form

A linear equation in slope-intercept form looks likey = mx + bwhere m and b are real numbers and m is the slope of the line. Get to know slope-intercept form, because it's going to be one...

#### Point-Slope Form

A line is in point-slope form if it looks likey – y1 = m(x – x1)where y1, x1, and m are real numbers. Here (x1, y1) is a fixed point on the line, and m is the slope of the line. (x1, y1)...

#### Quadratic Functions

We know what quadratic equations are. Now we're going to graph them. That's just how we roll. Whenever we find out what the Mega Millions lottery numbers are, we graph those, too. Same goes for bas...

#### Exponential Functions

The exponential functions we'll deal with here are functions of the formy = ab(linear function of x) + cwhere a and c are real numbers and b is greater than 1. Really, this just means we have a num...

#### Inequalities

An inequality is just a type of relation, which means we can graph it like we would graph any relation. The trick with inequalities is that, instead of drawing lines to connect the dots, we have to...