Guided Practice: Rates of Change in Linear and Quadratic Functions

🧭 Guided Practice

Pick an essential knowledge statement, then step through worked examples one move at a time.

1.3.A.1Concept

For a linear function, the average rate of change over any length input-value interval is constant.

ExampleThree intervals, one rate1 / 4

Let f(x) = 3x − 5. Find the average rate of change of f over [0, 2], [1, 5], and [−4, 10]. What do you notice?

Try it on paper first, then reveal each step to check your work.

Step 1 — Use the rate formula each time

Average rate of change over [a, b] = (f(b) − f(a)) / (b − a).