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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
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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**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.
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.
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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