Log In

My Passes

Sign Up
Learning Guides
Teacher Resources
Test Prep
College Readiness
Schools & Districts
All of Shmoop
Literature
Bible
Poetry
Shakespeare
Mythology
Bestsellers
Dr. Seuss
PreAlgebra
Algebra
Algebra II
Geometry
Biology
US History
Flashcards
DMV
Careers
SAT
ACT
AP Exams
En Español
Essay Lab
Videos
Literary Critics
Shmoop Shtuff
Cite This Page
To Go
Functions
Home
Algebra
Functions
Exercises
Intro
Topics
Examples
Exercises
Terms
Best of the Web
Quizzes
Handouts
Table of Contents
ADVERTISEMENT
Functions Exercises
Sets
A set is a collection of things. This sentence is a set of words. This paragraph is a set of sentences. This explanation is a set of excessive examples.To write down a set, we make a list...
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 ProblemH...
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...
SlopeIntercept Form
A linear equation in slopeintercept form looks likey = mx + bwhere m and b are real numbers and m is the slope of the line. Get to know slopeintercept form, because it's going to be one...
PointSlope Form
A line is in pointslope 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...
Need help with College?