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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Question
![The equation provided is:
\[ f(x) = \frac{x - 2}{x^2 - x - 30} \]
Below the equation is a coordinate plane with the x-axis and y-axis both labeled. The x-axis ranges from -12 to 12, while the y-axis ranges from -10 to 6.
This graph is set up for plotting the function \( f(x) \). To sketch the graph, find the values of \( x \) where the function is undefined by setting the denominator to zero and solving for \( x \).
Following are steps to identify the nature of the graph:
1. **Find x-values where the function is undefined**:
- Solve \( x^2 - x - 30 = 0 \) to find vertical asymptotes.
2. **Identify horizontal asymptotes**:
- Compare degrees of the numerator and denominator.
3. **Find x- and y-intercepts**:
- For x-intercepts, set \( f(x) = 0 \) and solve for \( x \).
- For the y-intercept, evaluate \( f(0) \).
Use these steps to fully understand and graph the function on the coordinate plane provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe92e694a-8dce-4f5c-a0b3-7db66cedb1e5%2F9e85df1b-87a9-4f59-a8a5-8f3599bc3f60%2Fnvano5d.jpeg&w=3840&q=75)
Transcribed Image Text:The equation provided is:
\[ f(x) = \frac{x - 2}{x^2 - x - 30} \]
Below the equation is a coordinate plane with the x-axis and y-axis both labeled. The x-axis ranges from -12 to 12, while the y-axis ranges from -10 to 6.
This graph is set up for plotting the function \( f(x) \). To sketch the graph, find the values of \( x \) where the function is undefined by setting the denominator to zero and solving for \( x \).
Following are steps to identify the nature of the graph:
1. **Find x-values where the function is undefined**:
- Solve \( x^2 - x - 30 = 0 \) to find vertical asymptotes.
2. **Identify horizontal asymptotes**:
- Compare degrees of the numerator and denominator.
3. **Find x- and y-intercepts**:
- For x-intercepts, set \( f(x) = 0 \) and solve for \( x \).
- For the y-intercept, evaluate \( f(0) \).
Use these steps to fully understand and graph the function on the coordinate plane provided.
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