4. Consider the function y = f (x) shown below to answer these questions: [= a. What is the domain of f ? Answer using set or interval notation, or state "all real numbers." b. What is the range of f ? Answer using set or interval notation, or state "all real numbers." c. Find the value of f (11). Approximate if necessary. d. Find all values of x such that f(x)=2. Approximate if necessary. 6- 5+ 3- 2+ -5 -4 -3 -2 -1 1 10 11 12 13 2+ 3-
4. Consider the function y = f (x) shown below to answer these questions: [= a. What is the domain of f ? Answer using set or interval notation, or state "all real numbers." b. What is the range of f ? Answer using set or interval notation, or state "all real numbers." c. Find the value of f (11). Approximate if necessary. d. Find all values of x such that f(x)=2. Approximate if necessary. 6- 5+ 3- 2+ -5 -4 -3 -2 -1 1 10 11 12 13 2+ 3-
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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![### Problem 4
Consider the function \( y = f(x) \) shown below to answer these questions:
a. What is the domain of \( f \)? Answer using set or interval notation, or state “all real numbers.”
b. What is the range of \( f \)? Answer using set or interval notation, or state “all real numbers.”
c. Find the value of \( f(11) \). Approximate if necessary.
d. Find all values of \( x \) such that \( f(x) = 2 \). Approximate if necessary.
### Graph Description
- The graph is a parabolic curve opening upwards.
- The endpoints of the curve are at \((-4,5)\) and \((13,5)\).
- The vertex, or the lowest point on the curve, is at approximately \((4.5,0)\).
- The grid lines indicate increments of 1 unit along both axes.
### Detailed Explanation
#### a. Domain of \( f \)
The domain is the set of all \( x \) values for which the function is defined. Observing the graph, the function starts at \( x = -4 \) and ends at \( x = 13 \), inclusive. Therefore, the domain is:
\[ [-4, 13] \]
#### b. Range of \( f \)
The range is the set of all \( y \) values that the function can take. From the graph, the lowest point on the y-axis is 0 (at the vertex), and the maximum y-value is 5 (at the endpoints). Thus, the range is:
\[ [0, 5] \]
#### c. Value of \( f(11) \)
To find \( f(11) \), look at the graph at \( x = 11 \). From observation, \( f(11) \) appears to be approximately 4.
#### d. Values of \( x \) such that \( f(x) = 2 \)
To find when \( f(x) = 2 \), we locate the points on the graph where \( y = 2 \). This occurs at approximately \( x = 2 \) and \( x = 7 \). Thus, the approximate solutions are:
\[ x \approx 2 \quad \text{and} \quad x \approx 7 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92d60e32-64a5-44cf-aeb7-142a324b6dde%2Fb4b8a762-9388-4d26-9ba6-3c1749065b93%2Faiatfby_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 4
Consider the function \( y = f(x) \) shown below to answer these questions:
a. What is the domain of \( f \)? Answer using set or interval notation, or state “all real numbers.”
b. What is the range of \( f \)? Answer using set or interval notation, or state “all real numbers.”
c. Find the value of \( f(11) \). Approximate if necessary.
d. Find all values of \( x \) such that \( f(x) = 2 \). Approximate if necessary.
### Graph Description
- The graph is a parabolic curve opening upwards.
- The endpoints of the curve are at \((-4,5)\) and \((13,5)\).
- The vertex, or the lowest point on the curve, is at approximately \((4.5,0)\).
- The grid lines indicate increments of 1 unit along both axes.
### Detailed Explanation
#### a. Domain of \( f \)
The domain is the set of all \( x \) values for which the function is defined. Observing the graph, the function starts at \( x = -4 \) and ends at \( x = 13 \), inclusive. Therefore, the domain is:
\[ [-4, 13] \]
#### b. Range of \( f \)
The range is the set of all \( y \) values that the function can take. From the graph, the lowest point on the y-axis is 0 (at the vertex), and the maximum y-value is 5 (at the endpoints). Thus, the range is:
\[ [0, 5] \]
#### c. Value of \( f(11) \)
To find \( f(11) \), look at the graph at \( x = 11 \). From observation, \( f(11) \) appears to be approximately 4.
#### d. Values of \( x \) such that \( f(x) = 2 \)
To find when \( f(x) = 2 \), we locate the points on the graph where \( y = 2 \). This occurs at approximately \( x = 2 \) and \( x = 7 \). Thus, the approximate solutions are:
\[ x \approx 2 \quad \text{and} \quad x \approx 7 \]
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