Shifting the Input
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 8 of 58.
The input can even contain x itself. f(x - 1) asks for the rule applied to x - 1. It looks strange at first, but the method is the same: every x in the rule becomes the whole input.
Take f(x) = x^2 + 4. Then f(x - 1) = (x - 1)^2 + 4. Expanding gives x^2 - 2x + 1 + 4, and collecting gives x^2 - 2x + 5. The new rule is a different function: it outputs at x what f outputs at x - 1.
You will meet this again in the graph chapters, where replacing x with x - 1 slides the whole graph one unit to the right. For now the job is algebra: substitute, expand, collect.
Challenge
For g(x) = x^2 - x, find g(x + 2), expanded and collected.
Try it yourself
Multiply everything out
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Functions & Transformations
4Combining Functions
Adding FunctionsSubtracting FunctionsMultiplying FunctionsAt a Single NumberRecap: Combining10Functions in Stories
Writing the RuleUsing the RuleWorking BackwardUndoing a ConversionRecap: Stories2Expressions as Inputs
A Letter as InputA Sum as InputShifting the InputSolving f(x) = kRecap: Inputs as Expressions5Composition
One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip