MathAdvanced MathMedium frequency
SAT Math: Average Rate of Change on a Curve
20+ practice questions in Praczo
What you need to know
The concept, explained
- 1
The average rate of change for any function f(x) over an interval [a, b] is just the slope of the secant line connecting those two points.
- 2
Formula: [f(b) - f(a)] / [b - a].
- 3
It is identical to the slope formula (y2 - y1) / (x2 - x1).
- 4
Even if a curve goes up and down wildly between x=a and x=b, the average rate of change only cares about the start and end heights.
Common mistakes
- ✗ Trying to calculate the instantaneous rate (derivative) rather than the average rate.
- ✗ Misreading the graph and plugging in the wrong y-values for the ends of the interval.
Try a sample question
SAT-style practice
Let f(x) = x² + 2. What is the average rate of change of f(x) over the interval x = 1 to x = 3?
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