Subtracting Functions
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 17 of 58.
Subtracting functions subtracts their outputs. Take p(x) = x^2 + 4x and q(x) = 3x - 5. Using both rules turns p(x) - q(x) into x^2 + 4x - (3x - 5), with q's whole rule in brackets.
The minus belongs to all of q, not only its first term. Taking away 3x - 5 means taking away 3x and taking away -5, which adds 5. So the line becomes x^2 + 4x - 3x + 5, and collecting gives x^2 + x + 5.
The usual slip is dropping the brackets and writing x^2 + 4x - 3x - 5. Check with x = 1: p(1) is 5 and q(1) is -2, so the difference is 7. The right rule gives 7; the slip gives -3.
Challenge
For f(x) = x^2 + 5 and g(x) = 2x - 3, find f(x) - g(x), multiplied out and collected. The minus takes away all of g.
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
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One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip