Adding Functions
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 16 of 58.
Two functions can be added to make a new one. The sum p(x) + q(x) means: give both functions the same input and add their outputs. Take p(x) = 2x + 5 and q(x) = x^2 + 3x.
Using both rules gives 2x + 5 + x^2 + 3x. Then collect like terms: 2x and 3x make 5x, so p(x) + q(x) = x^2 + 5x + 5.
Collecting matters because the new rule should do in one step what the two rules did in two. Check with x = 1: p(1) is 7 and q(1) is 4, so the sum is 11, and the new rule gives 1 + 5 + 5, which is 11 too.
Challenge
For f(x) = 3x + 2 and g(x) = x^2 - 4x, find f(x) + g(x) as one expression. Tap the two moves that use the rules, then type the sum with its like terms 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