The Range
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 14 of 58.
The range is the set of outputs a function actually produces. For f(x) = x^2 + 3, the square x^2 of a real number is never negative, so the smallest output comes at x = 0 and is 3. Every number from 3 upward is reached, so the range is y >= 3.
The same reasoning works for an absolute value. g(x) = |x| - 2 has |x| >= 0, so the outputs start at -2 and go up: the range is y >= -2.
A non-horizontal line is different: it goes on forever up and down, so its range is all real numbers. A horizontal line y = 4 has a range of just one number, 4.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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