At a Single Number
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 19 of 58.
Sometimes you need one value of a combination, such as p(4) - q(4). You do not need the combined rule for that: work out each function at 4, then combine the two numbers.
Take p(x) = x^2 - 2 and q(x) = 3x + 1. Putting 4 into both rules gives 4^2 - 2 - (3(4) + 1). Work out each part: p(4) is 14 and q(4) is 13, so the line becomes 14 - 13, which is 1.
Combining the rules first gives the same number: x^2 - 3x - 3 at 4 is 16 - 12 - 3, which is 1. Evaluating first is usually shorter, because numbers combine faster than expressions. The brackets around q's rule still matter: they keep all of q(4) subtracted.
Challenge
Use f(x) = x^2 + 1 and g(x) = 2x + 4 to work out f(3) - g(3). Tap the two moves that use the rules, then type the arithmetic line by line.
Try it yourself
Simplify the expression
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