The Hint text says, 'f(x) is a piecewise function, so we need to examine where each piece is undefined.' (and goes on from there). One or more of the questions is all about the domain for a piecewise function.

There is an exercise in the Algebra I content- 'Domain of a function' ( ). (old question kept for historical purposes) There were about 10 new modules added in the Algebra I 'Functions' section, I believe. These are a couple of the new modules added to address this: I believe those new modules added significant value to the lessons in that section of the KA content. Great job, Khan Academy! I am enjoying the new exercises, and I feel they really help fill in some small gaps that were there in the content.

So this piece wise stuff may seem arcane or just a very special (infrequent) case, but it is not, it is a fixture in the mathematical landscape, so enjoy the view!Įdit: The Algebra I section has been expanded to include some modules that fill in these gaps nicely, and a few others. Each phase, launch, staging, orbit insertion, course correction and docking is a piece that has a very different characteristics of fuel consumption, and will require a different expression with different variables (air resistance, weight, gravity, burn rates etc.) at each stage in order to model it correctly. Hmmm, something more scientific? How about modeling the fuel usage of a space shuttle from launch to docking with the ISS. Or perhaps your local video store: rent a game, $5/per game, rent 2-3 games, $4/game, rent more than 5 games, $3/per game.Īsk your folks about tax brackets, another piece-wise function. In your day to day life, a piece wise function might be found at the local car wash: $5 for a compact, $7.50 for a midsize sedan, $10 for an SUV, $20 for a Hummer. Where ever input thresholds (or boundaries) require significant changes in output modeling, you will find piece-wise functions.

Khan academy piecewise functions