Rates of Change in Linear and Quadratic Functions
Henry Lee
6 min read
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Study Guide Overview
This study guide covers rates of change in linear and quadratic functions. It explains calculating average rates of change, the difference between secant and tangent lines, and how concavity relates to the rate of change. It also includes practice questions and exam tips focusing on interpreting these concepts for linear and quadratic functions.
#AP Pre-Calculus: Rates of Change - The Night Before 🚀
Hey! Let's get you totally prepped for the exam. We're going to break down rates of change in linear and quadratic functions, making sure everything clicks. No stress, just clear understanding.
#1.3 Rates of Change in Linear and Quadratic Functions
#📈 Average Rates of Change
A linear function has a constant rate of change (slope), resulting in a straight line. A quadratic function has a changing rate of change, creating a curved graph.
- Linear Functions: The average rate of change is the same everywhere. It's the slope of the line!
- Quadratic Functions: The average rate of change isn't constant. It changes as you move along the curve.
Think of a linear function like a car going at a constant speed on a straight road. A quadratic function is like a car accelerating or decelerating – its speed changes. 🚗
The average rate of change over an interval [a, b] is the slope of the secant line connecting points (a, f(a)) and (b, f(b)).
Caption: A quadratic function's curve. Notice how the steepness changes.
Average rate of change = (change in output) / (chang...
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