Refer to the graph of the function f in the following figure. T YA 6543 4+ -2- X = 2 1 (a) Find f(0). f(0) = = X = (b) Find the value of x for which f(x) (i) f(x) = 3 (ii) f(x) = 0 X X X y = f(x) 5 6 = X 3 and f(x) = 0.
Refer to the graph of the function f in the following figure. T YA 6543 4+ -2- X = 2 1 (a) Find f(0). f(0) = = X = (b) Find the value of x for which f(x) (i) f(x) = 3 (ii) f(x) = 0 X X X y = f(x) 5 6 = X 3 and f(x) = 0.
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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![### Understanding the Graph of the Function \( f \)
#### Graph Description
The provided graph illustrates the function \( f(x) \). It plots the function on a coordinate system where the x-axis represents the independent variable \( x \) and the y-axis represents the dependent variable \( y \). The curve depicting \( y = f(x) \) starts at approximately \( (-2, -2) \) and rises to a peak before descending. Key points on the graph:
- It crosses the y-axis at approximately \( y = -1 \).
- The maximum value of the function occurs at \( x = 3 \), where \( f(3) = 6 \).
- The function crosses the x-axis at points \( x = 0 \) and \( x = 6 \), indicating the function values at these points are 0.
#### Questions and Answers
**(a) Find \( f(0) \).**
\[ f(0) = \]
The value of \( f(x) \) when \( x = 0 \) can be observed directly from the graph. At \( x = 0 \), the function value is approximately \( f(0) = -1 \).
**(b) Find the value of \( x \) for which \( f(x) = 3 \) and \( f(x) = 0 \).**
(i) \( f(x) = 3 \)
\[ x = \]
From the graph, the function \( f(x) \) attains the value 3 at two points - as it increases and then decreases. These points are \( x = 2 \) and approximately \( x = 4.5 \).
(ii) \( f(x) = 0 \)
\[ x = \]
From the graph, the function \( f(x) \) crosses the x-axis at two points, \( x = 0 \) and \( x = 6 \). These are the points where \( f(x) = 0 \).
### Summary
To succinctly summarize, the answers based on the observations from the graph are:
- \( f(0) = -1 \)
- When \( f(x) = 3 \), \( x = 2 \) or \( x \approx 4.5 \).
- When \( f(x) = 0 \), \( x = 0 \) or \( x = 6 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eeb6921-a110-4984-a04e-b3e01fc97c1d%2F6dcdefc6-375a-402b-bb92-b75b998ff965%2Fle2v6b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Graph of the Function \( f \)
#### Graph Description
The provided graph illustrates the function \( f(x) \). It plots the function on a coordinate system where the x-axis represents the independent variable \( x \) and the y-axis represents the dependent variable \( y \). The curve depicting \( y = f(x) \) starts at approximately \( (-2, -2) \) and rises to a peak before descending. Key points on the graph:
- It crosses the y-axis at approximately \( y = -1 \).
- The maximum value of the function occurs at \( x = 3 \), where \( f(3) = 6 \).
- The function crosses the x-axis at points \( x = 0 \) and \( x = 6 \), indicating the function values at these points are 0.
#### Questions and Answers
**(a) Find \( f(0) \).**
\[ f(0) = \]
The value of \( f(x) \) when \( x = 0 \) can be observed directly from the graph. At \( x = 0 \), the function value is approximately \( f(0) = -1 \).
**(b) Find the value of \( x \) for which \( f(x) = 3 \) and \( f(x) = 0 \).**
(i) \( f(x) = 3 \)
\[ x = \]
From the graph, the function \( f(x) \) attains the value 3 at two points - as it increases and then decreases. These points are \( x = 2 \) and approximately \( x = 4.5 \).
(ii) \( f(x) = 0 \)
\[ x = \]
From the graph, the function \( f(x) \) crosses the x-axis at two points, \( x = 0 \) and \( x = 6 \). These are the points where \( f(x) = 0 \).
### Summary
To succinctly summarize, the answers based on the observations from the graph are:
- \( f(0) = -1 \)
- When \( f(x) = 3 \), \( x = 2 \) or \( x \approx 4.5 \).
- When \( f(x) = 0 \), \( x = 0 \) or \( x = 6 \).
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