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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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