Sketch the graph of a function having the following properties: 1) The domain is all real numbers except x = 1. 2) It has an x-intercept at (−1, 0) and no others. It has a y-intercept of y = 1. 3) On the right, it has y = 1 as a horizontal asymptotes. On the left, it has y = −1 as a horizontal asymptotes. 4) It has a vertical asymptote at x = 1 and no others. 5) It is increasing on (−∞, 1) and decreasing on (1,∞). 6) It is always concave up.
Sketch the graph of a function having the following properties: 1) The domain is all real numbers except x = 1. 2) It has an x-intercept at (−1, 0) and no others. It has a y-intercept of y = 1. 3) On the right, it has y = 1 as a horizontal asymptotes. On the left, it has y = −1 as a horizontal asymptotes. 4) It has a vertical asymptote at x = 1 and no others. 5) It is increasing on (−∞, 1) and decreasing on (1,∞). 6) It is always concave up.
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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Sketch the graph of a function having the following properties:
1) The domain is all real numbers except x = 1.
2) It has an x-intercept at (−1, 0) and no others. It has a y-intercept of y = 1.
3) On the right, it has y = 1 as a horizontal asymptotes. On the left, it has y = −1 as a horizontal asymptotes.
4) It has a vertical asymptote at x = 1 and no others.
5) It is increasing on (−∞, 1) and decreasing on (1,∞).
6) It is always concave up.
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