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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Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Question

Transcribed Image Text:**Given the graph of f ''(x), which are possible graphs of f(x)?**
### Graph Descriptions:
1. **First Row - Graph of f ''(x):**
- The graph is a straight diagonal line with a positive slope that passes through the origin (0,0) and extends through the points (3,3) on the right and (-3,-3) on the left. This suggests a constant positive rate of change for f '(x), implying f(x) is a quadratic function.
2. **Second Row - Graphs of Possible f(x):**
- **Graph A (Left):**
- A cubic-shaped curve. It starts below the x-axis, moves up passing through the x-axis around x = -1, peaks near x = 0, then dips slightly before rising sharply.
- **Graph B (Right):**
- A sinusoidal-like curve shifted upwards. It starts slightly below the x-axis, dips near x = -1, rises and flattens towards x = 3.
3. **Third Row - Graphs of Possible f(x):**
- **Graph C (Left):**
- A cubic-shaped curve. It begins above the x-axis, descends crossing the x-axis around x = -1, reaches a minimum, and then ascends sharply.
- **Graph D (Right):**
- An S-shaped curve extending from the upper left to the lower right. It crosses the x-axis at around x = 0 and continues downward.
### Analysis:
- Since f ''(x) is positive, indicating concavity is upward, the possible f(x) graphs should be consistent with having sections of increasing slope, suggesting the correct candidate will exhibit a predominantly increasing behavior or show convexity on interval sections.
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