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Match the graphs with the functions. Each graph represents exactly one function and each function describes exactly one graph. X X z y X Z Answer Bank f(x, y) = cos (2) e-0.1(x+²) f (x, y) = x + lyl f (x, y) = cos (x - y) f (x, y) = 1+9+9 - +9y² f (x, y) = −1+x+y f(x, y) = cos (x² + y²)e-0.1(x²+²)

Match the graphs with the functions. Each graph represents exactly one function and each function describes exactly one graph. X X z y X Z Answer Bank f(x, y) = cos (2) e-0.1(x+²) f (x, y) = x + lyl f (x, y) = cos (x - y) f (x, y) = 1+9+9 - +9y² f (x, y) = −1+x+y f(x, y) = cos (x² + y²)e-0.1(x²+²)

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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### Graphs and Functions Matching Activity **Instructions:** Match the graphs with the functions from the Answer Bank below. Each graph represents exactly one function, and each function describes exactly one graph. **Graphs:** 1. **Graph 1:** - **Description:** This graph depicts a surface that slightly dips downwards in a symmetrical fashion from the center point. 2. **Graph 2:** - **Description:** This graph shows a wavy surface with periodic rises and falls, forming a unidirectional wave pattern. 3. **Graph 3:** - **Description:** This graph features a multi-peaked, wavelike surface. 4. **Graph 4:** - **Description:** This graph displays a V-shaped surface with a sharp ridge running along the x-axis. 5. **Graph 5:** - **Description:** This graph shows a flat plane surface that is slanted downward. 6. **Graph 6:** - **Description:** This graph features a dome-like surface with a symmetrical rise from the center. **Answer Bank:** 1. \( f(x, y) = \cos(y^2)e^{-0.1(x+y)} \) 2. \( f(x, y) = |x| + |y| \) 3. \( f(x, y) = \cos(x - y) \) 4. \( f(x, y) = \frac{1}{1+9x^2+9y^2} \) 5. \( f(x, y) = -\frac{1}{1+9x^2+y^2} \) 6. \( f(x, y) = \cos(x^2 + y^2)e^{-0.1(x+y)} \) **Diagrams Explanation:** - **Graph 1** pairs with the function: - **Graph 2** pairs with the function: - **Graph 3** pairs with the function: - **Graph 4** pairs with the function: - **Graph 5** pairs with the function: - **Graph 6** pairs with the function: Use the visual characteristics and the mathematical properties of the functions to find the appropriate matches.
Transcribed Image Text:### Graphs and Functions Matching Activity **Instructions:** Match the graphs with the functions from the Answer Bank below. Each graph represents exactly one function, and each function describes exactly one graph. **Graphs:** 1. **Graph 1:** - **Description:** This graph depicts a surface that slightly dips downwards in a symmetrical fashion from the center point. 2. **Graph 2:** - **Description:** This graph shows a wavy surface with periodic rises and falls, forming a unidirectional wave pattern. 3. **Graph 3:** - **Description:** This graph features a multi-peaked, wavelike surface. 4. **Graph 4:** - **Description:** This graph displays a V-shaped surface with a sharp ridge running along the x-axis. 5. **Graph 5:** - **Description:** This graph shows a flat plane surface that is slanted downward. 6. **Graph 6:** - **Description:** This graph features a dome-like surface with a symmetrical rise from the center. **Answer Bank:** 1. \( f(x, y) = \cos(y^2)e^{-0.1(x+y)} \) 2. \( f(x, y) = |x| + |y| \) 3. \( f(x, y) = \cos(x - y) \) 4. \( f(x, y) = \frac{1}{1+9x^2+9y^2} \) 5. \( f(x, y) = -\frac{1}{1+9x^2+y^2} \) 6. \( f(x, y) = \cos(x^2 + y^2)e^{-0.1(x+y)} \) **Diagrams Explanation:** - **Graph 1** pairs with the function: - **Graph 2** pairs with the function: - **Graph 3** pairs with the function: - **Graph 4** pairs with the function: - **Graph 5** pairs with the function: - **Graph 6** pairs with the function: Use the visual characteristics and the mathematical properties of the functions to find the appropriate matches.
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