(a) the domain of f (b) the range of f (c) the zero(s) of f (d) f(-1) (e) the intervals on which f is increasing (f) the intervals on which f is decreasing (g) the values for which f(x) ≤ 0 (h) any relative maxima or minima (i) the value(s) of x for which f(x) = 4 () Is f(4) positive or negative? La Thul L' WI D PA 2206
(a) the domain of f (b) the range of f (c) the zero(s) of f (d) f(-1) (e) the intervals on which f is increasing (f) the intervals on which f is decreasing (g) the values for which f(x) ≤ 0 (h) any relative maxima or minima (i) the value(s) of x for which f(x) = 4 () Is f(4) positive or negative? La Thul L' WI D PA 2206
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The educational content below is designed to help students analyze and understand the properties of functions using their graphs.
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### Analyzing the Graph of Function \( f \)
Using the graph of \( f \) (see the attached graph) to determine each of the following:
**(a) The domain of \( f \)**
The domain of \( f \) refers to all the possible input values (x-values) for which the function is defined. The graph extends from \( x = -6 \) to \( x = 6 \), suggesting that the domain is:
\[ [-6, 6] \]
**(b) The range of \( f \)**
The range of \( f \) refers to all the possible output values (y-values). From the graph, the minimum value of \( y \) is 0 and the maximum value is 6, suggesting the range is:
\[ [0, 6] \]
**(c) The zero(s) of \( f \)**
The zero(s) of \( f \) are the x-values where \( f(x) = 0 \). From the graph, the function crosses the x-axis at \( x = -4 \) and \( x = 2 \).
Zeroes of \( f \):
\[ -4, 2 \]
**(d) \( f(-1) \)**
To find \( f(-1) \), locate \( x = -1 \) on the graph and find the corresponding y-value. The graph suggests that \( f(-1) = 4 \).
\[ f(-1) = 4 \]
**(e) The intervals on which \( f \) is increasing**
A function is increasing on intervals where its graph goes upwards as we move to the right. From the graph, \( f \) is increasing on the interval:
\[ (-6, -2) \]
**(f) The intervals on which \( f \) is decreasing**
A function is decreasing on intervals where its graph goes downwards as we move to the right. From the graph, \( f \) is decreasing on the intervals:
\[ (-2, 6) \]
**(g) Values for which \( f(x) \leq 0 \)**
\( f(x) \leq 0 \) means the y-values are less than or equal to zero. From the graph](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc86e2b6-ce0f-4f58-b766-ef1d838098d3%2F40094f6b-969b-40e5-a920-d0d54b091d53%2F0fvnqh4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The educational content below is designed to help students analyze and understand the properties of functions using their graphs.
---
### Analyzing the Graph of Function \( f \)
Using the graph of \( f \) (see the attached graph) to determine each of the following:
**(a) The domain of \( f \)**
The domain of \( f \) refers to all the possible input values (x-values) for which the function is defined. The graph extends from \( x = -6 \) to \( x = 6 \), suggesting that the domain is:
\[ [-6, 6] \]
**(b) The range of \( f \)**
The range of \( f \) refers to all the possible output values (y-values). From the graph, the minimum value of \( y \) is 0 and the maximum value is 6, suggesting the range is:
\[ [0, 6] \]
**(c) The zero(s) of \( f \)**
The zero(s) of \( f \) are the x-values where \( f(x) = 0 \). From the graph, the function crosses the x-axis at \( x = -4 \) and \( x = 2 \).
Zeroes of \( f \):
\[ -4, 2 \]
**(d) \( f(-1) \)**
To find \( f(-1) \), locate \( x = -1 \) on the graph and find the corresponding y-value. The graph suggests that \( f(-1) = 4 \).
\[ f(-1) = 4 \]
**(e) The intervals on which \( f \) is increasing**
A function is increasing on intervals where its graph goes upwards as we move to the right. From the graph, \( f \) is increasing on the interval:
\[ (-6, -2) \]
**(f) The intervals on which \( f \) is decreasing**
A function is decreasing on intervals where its graph goes downwards as we move to the right. From the graph, \( f \) is decreasing on the intervals:
\[ (-2, 6) \]
**(g) Values for which \( f(x) \leq 0 \)**
\( f(x) \leq 0 \) means the y-values are less than or equal to zero. From the graph
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