Average Rate of Change
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 44 of 58.
A function's output changes as its input changes. The average rate of change measures how fast: the change in output divided by the change in input. Take f(x) = x^2 + 3x from x = 0 to x = 2. The output goes from f(0) = 0 to f(2) = 10, a change of 10, while the input changes by 2. So the rate is 10 over 2, which is 5: on average the output grows 5 for every 1 the input grows.
In general, from x = a to x = b the average rate of change is (f(b) - f(a))/(b - a). On the graph, (a, f(a)) and (b, f(b)) are two points, and this fraction is the slope of the straight line through them: rise over run.
Challenge
For f(x) = x^2 + 2x, find the average rate of change from x = 1 to x = 4. The board holds the fraction: tap the move that uses the rule once for each call, 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 Flip6Inverse Functions
Undoing a FunctionSwap and SolveFractions in InversesChecking an InverseA Value of the InverseRecap: Inverses9Rate of Change
Average Rate of ChangeA Line Keeps Its RateA Curve Changes RateVelocity as a RateRecap: Rate of Change