Modeling and Functions
Interact with functions by sliding their variables higher and lower to see what happens!
Use interactive graphing apps to explore and transform functions of all varieties: polynomials, exponents, logarithms, absolute value, and more. Learn a method of factoring not commonly taught in school, practice modeling scenarios, and do problem solving that reveals the beauty of mathematics.
Use experiments and play with graphs to learn algebra!
Interact with functions by sliding their variables higher and lower to see what happens!
Practice predicting the behavior of function transformations.
Explore factoring polynomials from a new perspective, and learn a new factoring technique.
Function notation, domain, range, and a plethora of graph types.
Review the definition of "function" and the notation used to represent functions.
Explore a variety of function types by experimenting and playing with their graphs.
Learn how the domains and ranges of functions depend on each other — and on the function types.
Strengthen your skills working with quadratic, cubic, exponential, and trigonometric functions.
Move any function around or change its shape with a fixed set of rules.
How can a function wind up stretched and transposed up, down, left, or right on the plane?
Throw some negatives into the mix and see what happens!
What happens when the input becomes the output and the output becomes the input?
First apply one function and then another, how does the initial input relate to the final output?
Explore the close connection between composing functions and applying internal function transformations.
Explore exponents and roots of all kinds.
Explore a fast-growing power function used to model growth in finance and biology.
What happens when the exponent is less than 1?
What happens when the exponent isn't an integer?
This simplification technique lets you move and remove radicals.
Solve some unusual problems where the functions are defined as infinite compositions of square roots.
Here you'll find every degree from zero to infinity.
Get a feel for how polynomials work by interacting with their graphs.
Solidify your understanding of how the graphs of polynomials are related to their functions.
Sometimes a bit of reflection can make things a lot easier.
Apply quadratics to study and draw conclusions about these flying and falling objects!
Practice adding, subtracting, and multiplying polynomials.
Split polynomials down to their smallest parts!
Explore the art of factoring polynomials from new, graphical perspectives.
Master the techniques for quadratic factoring!
Expand your factoring skills to cover cases where the leading coefficient is greater than 1.
Apply one of the most famous formulas in early mathematics to factor some polynomials.
Learn how to divide by polynomials using a technique similar to what's used in arithmetic with numbers.
Combine all of the techniques you've learned to tackle a variety of challenging polynomial problems.
Learn how to apply Pascal's triangle to quickly expand binomials.
Put together two polynomials with division, and a new world opens up.
When one variable goes up, does the other go up with it?
Explore what variation looks like when larger powers are involved.
Get closer and closer and closer... to infinity.
Learn how to tackle these tricky horizontal and slant asymptote cases!
Combine all of the techniques you've learned so far to solve these rational function problems.
Make new functions by mashing together old ones.
What are absolute value functions and how does arithmetic interact with them?
Consider some real-life scenarios where the concept of absolute value applies.
Practice and strengthen your skills by solving some challenging absolute value problems.
Create Frankenstein functions out of the pieces of spliced-up common functions!
Explore functions defined by the operation of rounding down or up to the nearest integer.