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Sketch the graph of a continuous function f with all of the following properties: (i) f(0) = 2 (ii) f(x) is decreasing for 0 ≤ x ≤ 3 (iii) f(x) is increasing for 3 < x < 5 (iv) f(x) is decreasing for > 5 (v) f(x) → 9 as x → ∞

Sketch the graph of a continuous function f with all of the following properties: (i) f(0) = 2 (ii) f(x) is decreasing for 0 ≤ x ≤ 3 (iii) f(x) is increasing for 3 < x < 5 (iv) f(x) is decreasing for > 5 (v) f(x) → 9 as x → ∞

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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**Title: Sketching a Continuous Function with Given Properties** **Instructions:** Sketch the graph of a continuous function \( f \) with all the following properties: 1. \( f(0) = 2 \) 2. \( f(x) \) is decreasing for \( 0 \leq x \leq 3 \) 3. \( f(x) \) is increasing for \( 3 < x \leq 5 \) 4. \( f(x) \) is decreasing for \( x > 5 \) 5. \( f(x) \to 9 \) as \( x \to \infty \) **Discussion:** - **Initial Value**: The function starts at \( f(0) = 2 \). - **Decreasing Interval**: From \( x = 0 \) to \( x = 3 \), the function decreases, indicating a downward slope. - **Increasing Interval**: Between \( x = 3 \) and \( x = 5 \), the function increases, showing an upward slope. - **Decreasing After \( x = 5 \)**: For values \( x > 5 \), the function decreases again. - **End Behavior**: As \( x \) approaches infinity, the function approaches the value 9. By understanding and combining these characteristics, you can construct the graph of the function visually, ensuring all specified properties are fulfilled in the representation.
Transcribed Image Text:**Title: Sketching a Continuous Function with Given Properties** **Instructions:** Sketch the graph of a continuous function \( f \) with all the following properties: 1. \( f(0) = 2 \) 2. \( f(x) \) is decreasing for \( 0 \leq x \leq 3 \) 3. \( f(x) \) is increasing for \( 3 < x \leq 5 \) 4. \( f(x) \) is decreasing for \( x > 5 \) 5. \( f(x) \to 9 \) as \( x \to \infty \) **Discussion:** - **Initial Value**: The function starts at \( f(0) = 2 \). - **Decreasing Interval**: From \( x = 0 \) to \( x = 3 \), the function decreases, indicating a downward slope. - **Increasing Interval**: Between \( x = 3 \) and \( x = 5 \), the function increases, showing an upward slope. - **Decreasing After \( x = 5 \)**: For values \( x > 5 \), the function decreases again. - **End Behavior**: As \( x \) approaches infinity, the function approaches the value 9. By understanding and combining these characteristics, you can construct the graph of the function visually, ensuring all specified properties are fulfilled in the representation.
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