Sketching a Function A Sketch the graph of a single function f(x) that satisfies all of the following conditions: 1. The domain of f is (-∞0, 0) U (0,00) 2. lim f(x) = -2 2 3. The only vertical asymptote that f has is at x = -3 4. lim f(x) = 0, but f is not continuous at x = -1 24-1 5. f(3) = 1, lim f(x) = 1, but f is not continuous at x = 3 +31 6. lim f(x) = f(5) 2-5 Give a written justification for why your graph meets the conditions above. Additionally, remember that your graph is supposed to be a graph of a function. Functions all have to pass a certain test!
Sketching a Function A Sketch the graph of a single function f(x) that satisfies all of the following conditions: 1. The domain of f is (-∞0, 0) U (0,00) 2. lim f(x) = -2 2 3. The only vertical asymptote that f has is at x = -3 4. lim f(x) = 0, but f is not continuous at x = -1 24-1 5. f(3) = 1, lim f(x) = 1, but f is not continuous at x = 3 +31 6. lim f(x) = f(5) 2-5 Give a written justification for why your graph meets the conditions above. Additionally, remember that your graph is supposed to be a graph of a function. Functions all have to pass a certain test!
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:**Sketching a Function**
Sketch the graph of a single function \( f(x) \) that satisfies all of the following conditions:
1. The domain of \( f \) is \( (-\infty, 0) \cup (0, \infty) \)
2. \( \lim_{{x \to 2}} f(x) = -2 \)
3. The only vertical asymptote that \( f \) has is at \( x = -3 \)
4. \( \lim_{{x \to -1^-}} f(x) = 0 \), but \( f \) is not continuous at \( x = -1 \)
5. \( f(3) = 1 \), \( \lim_{{x \to 3^-}} f(x) = 1 \), but \( f \) is not continuous at \( x = 3 \)
6. \( \lim_{{x \to 5}} f(x) = f(5) \)
Give a written justification for why your graph meets the conditions above. Additionally, remember that your graph is supposed to be a graph of a *function*. Functions all have to pass a certain test!
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