Operations on functions graphically

A.B. Cron has created a series of GeoGebra applets that demonstrate operations on functions graphically. You can enter any two functions (f and g) and then, from their graphs, determine points that will be on the graph of, for example, h = f + g. After plotting a number of points, you can check the box to show the graph of h to check your work. The adding functions applet has links to the applets for subtracting, multiplying, dividing, and composition.

(Links updated 7/30/2016)

Finding logs

This is a clean, simple applet by Michael Borcherds that provides practice finding logs. It keeps track of how many you got right on the first try and how much time you've spent. To restart the count, refresh the page.

Inverse functions graphically

Taylor Russell's inverse function applet provides a very nice visualization of the fact that the graph of an inverse function is obtained by switching the x- and y-coordinates of every point. You input the original function, so it is extremely flexible. As an added bonus, you can also plot the reciprocal function and see that it is not the same as the inverse. I used this applet in combination with Emily Alman's Joe the Math Guy comic for my most successful introduction to inverse functions ever.

Mathmo

Mathmo is a review tool for A-level maths developed by the NRICH project at the University of Cambridge. It is advertised to work in Chrome, Safari, and on mobile devices. There are questions on wide range of topics in a typical American high school curriculum, though the range of question types within a topic is very limited. In some topics (logarithms, for example) there are a few different types of questions, but in most there is a single question type where just the specifics (numbers, functions, etc.) vary. You can ask for random questions from the wide range of syllabus topics or can choose your own specific topics to build up a set of questions. You work the problems on paper (or in your head) and then push the check answer button to compare your answer with the given one. If you want several questions on the same topic, you can add the topic multiple times to your question list or can click the new button from within a particular question.

I did experience a couple of minor bugs. Sometimes, the first time you look at a question you see the code rather than the mathematical notation. Clicking (or tapping) the question changes the code to notation. The description says that the color of the question changes once you indicate whether you got the question right or wrong. I didn't experience that either on the iPad or in Chrome.