Multiplying Functions
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 18 of 58.
Multiplying functions multiplies their outputs. For p(x) = x + 4 and q(x) = x - 1, using both rules turns p(x) × q(x) into (x + 4)(x - 1). Each rule gets its own brackets, because the whole output of p multiplies the whole output of q.
Then multiply out as in Algebra: every term of the first bracket times every term of the second. That gives x^2 - x + 4x - 4, and collecting leaves x^2 + 3x - 4.
Without the brackets, x + 4x - 1 would multiply only the 4 by x, which is a different function. Check with x = 2: p(2) is 6 and q(2) is 1, so the product is 6, and 4 + 6 - 4 is 6 as well.
Challenge
For f(x) = x + 3 and g(x) = x - 2, find f(x) × g(x), multiplied out 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