Using the Rule
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 50 of 58.
Once a story has a rule, the rule answers questions about the story. The music school's cost for n lessons is C(n) = 25 + 10n dollars. What do 6 lessons cost? Evaluate: C(6) = 25 + 10(6), which is 25 + 60, so 85 dollars.
Read the answer back into the story with its units. The input 6 is a number of lessons and the output 85 is a number of dollars. Six lessons, fee included, cost 85 dollars.
A story also sets the domain. n counts lessons, so it can be 0, 1, 2 and so on, but never -2 or 2.5. The rule would happily work out C(2.5), but no one buys half a lesson, so that output means nothing.
Challenge
A climbing gym's cost for n visits is C(n) = 15 + 4n dollars. Work out C(12), the cost of 12 visits. Use the rule, 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