f is increasing on: f is decreasing on: f is concave up on: f is concave down on: f has horizontal asymptote(s): ƒ has vertical asymptote(s):
f is increasing on: f is decreasing on: f is concave up on: f is concave down on: f has horizontal asymptote(s): ƒ has vertical asymptote(s):
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:**Consider the function \( f(x) = \frac{x - 2}{x - 8} \).**
**Use the graphing utility to graph \( f \).**
### Graph Description:
- The graph is shown on a Cartesian plane with both x and y axes ranging from -20 to 20.
- There is a grid overlay with equal intervals providing reference points for plotting.
- The graphing tool interface includes a text box labeled \( f(x) = \) where users can enter the function for visualization.
- There are zoom-in (+) and zoom-out (-) buttons on the top right of the graph for adjusting the view.
- This graphing utility is powered by Desmos, a popular online graphing tool.
To understand and visualize the behavior of the function \( f(x) = \frac{x - 2}{x - 8} \), input it into the graphing utility. Notice aspects like intercepts, vertical and horizontal asymptotes, and overall shape of the function based on the rational expression.
![**Analysis of Function Characteristics**
- **\( f \) is increasing on:**
[Enter intervals where \( f \) is increasing]
- **\( f \) is decreasing on:**
[Enter intervals where \( f \) is decreasing]
- **\( f \) is concave up on:**
[Enter intervals where \( f \) is concave up]
- **\( f \) is concave down on:**
[Enter intervals where \( f \) is concave down]
- **\( f \) has horizontal asymptote(s):**
[Enter the equations of the horizontal asymptotes]
- **\( f \) has vertical asymptote(s):**
[Enter the equations of the vertical asymptotes]
> Use these guidelines to examine the behavior and characteristics of the function \( f \). Fill in the respective fields as you analyze the specific properties related to intervals of increase, decrease, concavity, and asymptotic behavior.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44bcc854-a672-4b6c-b0fb-367be49d6297%2Fa77e5dca-8316-45bc-a4df-e232a9fd9fac%2Fzknsn4f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Analysis of Function Characteristics**
- **\( f \) is increasing on:**
[Enter intervals where \( f \) is increasing]
- **\( f \) is decreasing on:**
[Enter intervals where \( f \) is decreasing]
- **\( f \) is concave up on:**
[Enter intervals where \( f \) is concave up]
- **\( f \) is concave down on:**
[Enter intervals where \( f \) is concave down]
- **\( f \) has horizontal asymptote(s):**
[Enter the equations of the horizontal asymptotes]
- **\( f \) has vertical asymptote(s):**
[Enter the equations of the vertical asymptotes]
> Use these guidelines to examine the behavior and characteristics of the function \( f \). Fill in the respective fields as you analyze the specific properties related to intervals of increase, decrease, concavity, and asymptotic behavior.
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