AP Precalculus Topics 1.1–1.3 Flashcards

Vocabulary practice flashcards covering rates of change, concavity, function behavior, and graph analysis for AP Precalculus.

Average Rate of Change

The measure of how much a function output changes per unit of input over a specified interval $[a, b]$, calculated using the formula $\frac{f(b) - f(a)}{b - a}$.

Positive Rate of Change

A rate of change indicating that as the input variable $x$ increases, the function output $f(x)$ also increases.

Negative Rate of Change

A rate of change indicating that as the input variable $x$ increases, the function output $f(x)$ decreases.

Concave Up

The graphical property where a function's curve bends upward over an interval, meaning the function's rate of change is increasing.

Concave Down

The graphical property where a function's curve bends downward over an interval, meaning the function's rate of change is decreasing.

Point of Inflection

A point on the graph of a function at which the concavity changes from concave up to concave down or from concave down to concave up.

Increasing at an Increasing Rate

The behavior of a function $f(x)$ that is rising ($f(x)$ is increasing) and concave up, meaning its rate of change is positive and increasing.

Increasing at a Decreasing Rate

The behavior of a function $g(x)$ that is rising ($g(x)$ is increasing) and concave down, meaning its rate of change is positive and decreasing.

Decreasing at an Increasing Rate

The behavior of a function $f(x)$ that is falling ($f(x)$ is decreasing) and concave up, meaning its rate of change is negative and increasing.

Decreasing at a Decreasing Rate

The behavior of a function $p(x)$ that is falling ($p(x)$ is decreasing) and concave down, meaning its rate of change is negative and decreasing.

Tangent Line Slope

The slope of a line tangent to a curve at a given point, representing the instantaneous rate of change of the function at that specific point.

Extrema

The local or absolute maximum and minimum points on a function's graph where the function changes direction between increasing and decreasing.

Table-Based Average Rate of Change

The calculation of $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$ using discrete coordinate pairs $(x_1, f(x_1))$ and $(x_2, f(x_2))$ provided in a data table.