AP Pre-Calculus Rates of Change and Concavity Vocabulary

Vocabulary practice flashcards covering functions, rates of change, concavity, points of inflection, and table analysis from AP Pre-Calculus notes.

Concave Up

A characteristic of a function over an interval where its rate of change is increasing.

Concave Down

A characteristic of a function over an interval where its rate of change is decreasing.

Point of Inflection

A point on a graph where the rate of change turns from increasing to decreasing or vice-versa, signifying a change in concavity.

Average Rate of Change (AROC)

The measure of how much a function changes per unit on average over a closed interval $[x_1, x_2]$, calculated as $m = \frac{\Delta Y}{\Delta X} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$.

Linear Table Identification

A table of values represents a linear function if the rate of change $m = \frac{\Delta Y}{\Delta X}$ is constant across all input intervals.

Quadratic Table Identification

A table of values represents a quadratic function if the rate of change $m = \frac{\Delta Y}{\Delta X}$ changes at a constant rate.

Increasing Function Interval

An interval where the output values $y = f(x)$ of a graph move upward from left to right as input values $x$ increase.

Decreasing Function Interval

An interval where the output values $y = f(x)$ of a graph move downward from left to right as input values $x$ increase.

Positive Rate of Change Scenarios

Relationships where an increase in one variable corresponds to an increase in another, such as height of a growing tree over time or a child's age versus height.

Negative Rate of Change Scenarios

Relationships where an increase in one variable corresponds to a decrease in another, such as remaining volume in a water container over time or a golfer's skill level versus score.

Concavity vs. Function Increasing Distinction

An interval where a function is concave up indicates that its rate of change is increasing over that interval, which is distinct from the function graph's output values $y = f(x)$ increasing.

Instantaneous Rate of Change Estimation

The method of approximating the rate of change at a single point $t$ by calculating average rates of change over progressively smaller intervals surrounding $t$.