AP Precalculus Topic 1.1 - Change in Tandem

Vocabulary and problem analysis flashcards for AP Precalculus Worksheet A Topic 1.1 on Change in Tandem.

Change in Tandem

The mathematical concept of analyzing how two quantities change simultaneously relative to each other, such as examining how a function $h(t)$ and its rate of change behave across specific intervals.

Midline of a Periodic Function

The horizontal reference line located halfway between the maximum and minimum values of a periodic function graph.

Worksheet A Topic 1.1 Overview

A practice worksheet created by Bryan Passwater for AP Precalculus covering function behavior, midlines, and rates of change over periodic cycles.

Problem 1: Behavior of $h$ on $(t_1, t_2)$

Where $t_1$ is the $t$-coordinate of $G(-5,9)$ and $t_2$ is the $t$-coordinate of $J(-4,7)$, the function $h$ is positive and decreasing on the interval $(t_1, t_2)$.

Problem 1: Rate of Change of $h$ on $(t_1, t_2)$

On the interval from $G(-5,9)$ to $J(-4,7)$, the rate of change of $h$ is negative and increasing (becoming less steep towards the minimum at $J$).

Problem 2: Labeled Points and Midline

A periodic graph of $h(t)$ featuring points $F(-4,0)$, $G(-2,-2.1)$, $J(0,-4.2)$, $K(2,-2.1)$, and $P(4,0)$, with a midline equation of $y = -2.1$.

Problem 2: Behavior of $h$ on $(t_1, t_2)$

Where $t_1$ is the $t$-coordinate of $K(2,-2.1)$ and $t_2$ is the $t$-coordinate of $P(4,0)$, the function $h$ is negative and increasing on the interval $(t_1, t_2)$.

Problem 3: Behavior of $h$ on $(t_1, t_2)$

Where $t_1$ is the $t$-coordinate of $F(0,6)$ and $t_2$ is the $t$-coordinate of $G(0.5,1)$, the function $h$ is positive and decreasing on the interval $(t_1, t_2)$.