No Dividing by Zero
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 12 of 58.
A rule with a fraction loses every input that makes its denominator zero. To find them, set the denominator equal to zero and solve. For f(x) = 5/(x - 3), the equation x - 3 = 0 gives 3, so 3 is the one input f refuses.
The numerator does not matter here. Zero on top is fine: 0/4 is just 0. Only zero underneath breaks the rule.
For g(x) = 1/(3x - 6), solve 3x - 6 = 0: 3x is 6, so x is 2. The domain of g is every real number except 2.
Challenge
The function f(x) = 7/(2x + 8) refuses one input. The board shows its denominator set to zero: solve it to find that input.
Try it yourself
Solve for x
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