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a. Drawone graph of the following Properties: function t Satisfies all pe OE of Idemain 2) of f is all reals of f ís all seals s5 2(ange of f is all reals 55 3) FG5=2 4) f(4)= -| 5) lim f does exist %3D not

a. Drawone graph of the following Properties: function t Satisfies all pe OE of Idemain 2) of f is all reals of f ís all seals s5 2(ange of f is all reals 55 3) FG5=2 4) f(4)= -| 5) lim f does exist %3D not

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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# Problem Statement ## a. Draw one graph of a function \( f \) that satisfies all six of the following properties: 1. **Domain of \( f \) is all reals.** 2. **Range of \( f \) is all reals \(\leq 5\).** 3. **\( f(3) = 2 \)** 4. **\( f(4) = -1 \)** 5. **\( \lim_{{x \to 1}} f(x) \) does not exist** 6. **\( \lim_{{x \to 4}} f(x) = 0 \)** ## b. For your graph above, at which x-values is \( f \) discontinuous and what types are they? ### Explanation of the Diagrams or Graphs Please create a graph that represents these properties: - **Discontinuity at \( x = 1 \):** Indicating the limit does not exist here, which could be shown by a jump or oscillation. - **Approach 0 as \( x \to 4 \):** Ensuring that, near \( x = 4 \), the function approaches zero, but the function value at \( x = 4 \) is \(-1\). Ensure the graph fulfills the given range and domain conditions and note where the function is discontinuous. Discuss the types of discontinuities (such as jump, infinite, or removable) in context.
Transcribed Image Text:# Problem Statement ## a. Draw one graph of a function \( f \) that satisfies all six of the following properties: 1. **Domain of \( f \) is all reals.** 2. **Range of \( f \) is all reals \(\leq 5\).** 3. **\( f(3) = 2 \)** 4. **\( f(4) = -1 \)** 5. **\( \lim_{{x \to 1}} f(x) \) does not exist** 6. **\( \lim_{{x \to 4}} f(x) = 0 \)** ## b. For your graph above, at which x-values is \( f \) discontinuous and what types are they? ### Explanation of the Diagrams or Graphs Please create a graph that represents these properties: - **Discontinuity at \( x = 1 \):** Indicating the limit does not exist here, which could be shown by a jump or oscillation. - **Approach 0 as \( x \to 4 \):** Ensuring that, near \( x = 4 \), the function approaches zero, but the function value at \( x = 4 \) is \(-1\). Ensure the graph fulfills the given range and domain conditions and note where the function is discontinuous. Discuss the types of discontinuities (such as jump, infinite, or removable) in context.
Expert Solution
Step 1

given conditions

1) domain of f is all real 

2) range of f is all real less than 5

3) f1=2

4) f4=-1

5) limx→1 fx does not exist

6) limx→4 fx=0

 

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