The graph of f(t) is given below. f(t) a b Match the graph below with one of the functions. a b Of(t)-f(t)u(ta) Of(t-b)u(t- b) Of(t)u(ta) Of(t)-f(t)u(t - b) Of(t)u(ta) f(t)u(t - b) Of(ta)u(ta)-f(ta)U(t - b)
The graph of f(t) is given below. f(t) a b Match the graph below with one of the functions. a b Of(t)-f(t)u(ta) Of(t-b)u(t- b) Of(t)u(ta) Of(t)-f(t)u(t - b) Of(t)u(ta) f(t)u(t - b) Of(ta)u(ta)-f(ta)U(t - b)
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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![The graph of \( f(t) \) is given below.
![Graph of \( f(t) \)]
The graph has a smooth curve, starting with a steep ascent, reaching a peak before decreasing and then rising again to another peak, eventually tapering off. It is plotted against the \( t \)-axis with marked points \( a \) and \( b \).
**Match the graph below with one of the functions.**
![Graph to Match]
This second graph presents a curve initially ascending to a peak, followed by a sharp descent to zero on point \( a \), then a horizontal line along the \( t \)-axis to point \( b \).
**Function Options:**
- \( \circ \quad f(t) - f(t)\chi(t-a) \)
- \( \circ \quad f(t-b)\chi(t-b) \)
- \( \circ \quad f(t)\chi(t-a) \)
- \( \circ \quad f(t) - f(t)\chi(t-b) \)
- \( \circ \quad f(t)\chi(t-a) - f(t)\chi(t-b) \)
- \( \circ \quad f(t-a)\chi(t-a) - f(t-a)\chi(t-b) \)
*Note:* \( \chi \) denotes the characteristic function, which is typically defined as a function equal to 1 when the condition is met and 0 otherwise. Consider how each function reflects changes in the original graph of \( f(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe462800b-ac16-4590-bafb-82d68c005ec5%2F34b390b6-147c-4df4-ba23-00daf6f3e9d3%2F09gnob9_processed.png&w=3840&q=75)
Transcribed Image Text:The graph of \( f(t) \) is given below.
![Graph of \( f(t) \)]
The graph has a smooth curve, starting with a steep ascent, reaching a peak before decreasing and then rising again to another peak, eventually tapering off. It is plotted against the \( t \)-axis with marked points \( a \) and \( b \).
**Match the graph below with one of the functions.**
![Graph to Match]
This second graph presents a curve initially ascending to a peak, followed by a sharp descent to zero on point \( a \), then a horizontal line along the \( t \)-axis to point \( b \).
**Function Options:**
- \( \circ \quad f(t) - f(t)\chi(t-a) \)
- \( \circ \quad f(t-b)\chi(t-b) \)
- \( \circ \quad f(t)\chi(t-a) \)
- \( \circ \quad f(t) - f(t)\chi(t-b) \)
- \( \circ \quad f(t)\chi(t-a) - f(t)\chi(t-b) \)
- \( \circ \quad f(t-a)\chi(t-a) - f(t-a)\chi(t-b) \)
*Note:* \( \chi \) denotes the characteristic function, which is typically defined as a function equal to 1 when the condition is met and 0 otherwise. Consider how each function reflects changes in the original graph of \( f(t) \).
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