The graph below shows the relationship between the height of the water in a bottle (in inches), h, and the volume of water in the bottle (in cups), V.
The graph below shows the relationship between the height of the water in a bottle (in inches), h, and the volume of water in the bottle (in cups), V.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:**Graph Description and Analysis:**
The graph illustrates the relationship between the height of the water in a bottle (in inches), denoted as \( h \), and the volume of water in the bottle (in cups), denoted as \( V \).
- The horizontal axis represents the volume of water \( V \) in cups.
- The vertical axis represents the height of the water \( h \) in inches.
- The graph starts at the origin and exhibits a curvilinear trajectory, indicating a non-linear relationship between \( h \) and \( V \).
**Graph Characteristics:**
- Initially, for small changes in the volume \( V \), the height \( h \) increases slowly.
- As \( V \) increases, the rate of increase in \( h \) becomes more pronounced, indicating that the height grows faster with additional increases in volume.
**Question and Options:**
The question asks to describe how the height of the water in the bottle varies with the volume over the interval \( V = 0 \) to \( V = 1.5 \).
**Options:**
1. For successive equal changes in \( V \), the height of the water increases by equal amounts.
2. For successive equal changes in \( V \), the height of the water increases by less and less.
3. For successive equal changes in \( V \), the height of the water increases by more and more.
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