Negative Inputs
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 4 of 58.
A negative input is where most slips happen. Take f(x) = x^2 + 3x and the input -2. Replacing x gives (-2)^2 + 3(-2): every x becomes the whole input, sign included, in brackets.
The brackets matter. (-2)^2 is -2 times -2, which is 4. Without them, -2^2 means the negative of 2 squared, which is -4. Then 3(-2) is -6. So the arithmetic is 4 - 6, and f(-2) = -2.
A good habit is to write the two terms separately first, each with its sign worked out, and only then combine them. One line per step keeps each sign visible.
Challenge
Use h(x) = x^2 - 2x to work out h(-3).
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