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Using the graph of f (x) shown below, match the functions (i)-(v) with a graph (a)-(e). (i) y = f(-x) matches (ii) y = - f(x) matches (iv) y = (b) (c) (iii) y = f(-x) + 3 matches f(x - 1) matches (d) (e) (v) y = f(-x) matches (a) (a) (c) (e) f(x) * t." t (b) +++ (d) +

Using the graph of f (x) shown below, match the functions (i)-(v) with a graph (a)-(e). (i) y = f(-x) matches (ii) y = - f(x) matches (iv) y = (b) (c) (iii) y = f(-x) + 3 matches f(x - 1) matches (d) (e) (v) y = f(-x) matches (a) (a) (c) (e) f(x) * t." t (b) +++ (d) +

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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**Instructions:** Using the graph of \( f(x) \) shown, match the functions (i)-(v) with a graph (a)-(e). **Graphs:** 1. **Original Graph:** - The graph labeled \( f(x) \) is a curve with a section that dips below the x-axis and then rises above it, similar to a small wave or dip. 2. **Options:** - **(a):** A reflection of the original graph across the x-axis. - **(b):** A reflection of the original graph across the y-axis. - **(c):** A linear transformation descending from left to right, going through the origin. - **(d):** The original graph shifted upwards by 3 units. - **(e):** The original graph reflected across the y-axis and shifted to the right by 1 unit. **Matching Functions:** (i) \( y = f(-x) \) matches **(b)**. (ii) \( y = -f(x) \) matches **(a)**. (iii) \( y = f(-x) + 3 \) matches **(d)**. (iv) \( y = -f(x-1) \) matches **(e)**. (v) \( y = -f(-x) \) matches **(c)**.
Transcribed Image Text:**Instructions:** Using the graph of \( f(x) \) shown, match the functions (i)-(v) with a graph (a)-(e). **Graphs:** 1. **Original Graph:** - The graph labeled \( f(x) \) is a curve with a section that dips below the x-axis and then rises above it, similar to a small wave or dip. 2. **Options:** - **(a):** A reflection of the original graph across the x-axis. - **(b):** A reflection of the original graph across the y-axis. - **(c):** A linear transformation descending from left to right, going through the origin. - **(d):** The original graph shifted upwards by 3 units. - **(e):** The original graph reflected across the y-axis and shifted to the right by 1 unit. **Matching Functions:** (i) \( y = f(-x) \) matches **(b)**. (ii) \( y = -f(x) \) matches **(a)**. (iii) \( y = f(-x) + 3 \) matches **(d)**. (iv) \( y = -f(x-1) \) matches **(e)**. (v) \( y = -f(-x) \) matches **(c)**.
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