1. A function f(t) is called periodic if there exists a positive constant T such that:
A.
f(t + T) = f(t) for all values of t
B.
f(t + T) = 0 for all values of t
C.
f(t + T) = -f(t) for all values of t
D.
f(t + T) = t for all values of t
Correct Answer:
f(t + T) = f(t) for all values of t
Explanation:
A function is periodic when it repeats its values after a fixed positive interval T, so f(t + T) equals f(t) for every t.
2. In the definition of a periodic function, the quantity T represents the:
A.
Amplitude
B.
Period
C.
Frequency
D.
Initial value
Correct Answer:
Period
Explanation:
The period T is the smallest positive interval after which the function repeats its values.
3. Which condition must be satisfied by a periodic function with period T?
A.
T must be negative
B.
T must be zero
C.
T must be positive
D.
T must change continuously
Correct Answer:
T must be positive
Explanation:
By definition, the period is a positive constant interval of repetition.
4. If f(t + 4) = f(t) for every value of t, then 4 is a:
A.
Possible period of f(t)
B.
Maximum value of f(t)
C.
Minimum value of f(t)
D.
Starting value of f(t)
Correct Answer:
Possible period of f(t)
Explanation:
Since the function has the same value after an interval of 4, 4 is a period of the function.
5. A periodic function repeats its values after:
A.
An irregular interval
B.
A fixed interval
C.
An interval that is always zero
D.
An interval that continuously increases
Correct Answer:
A fixed interval
Explanation:
Periodic behavior means that the function repeats after a constant, fixed interval called its period.
6. If a function satisfies f(t + T) = f(t), what does this indicate?
A.
The function is periodic with period T
B.
The function is always increasing
C.
The function is always zero
D.
The function has no repeated values
Correct Answer:
The function is periodic with period T
Explanation:
The equation f(t + T) = f(t) is the defining condition for periodicity.
7. Which of the following best describes the period of a function?
A.
The shortest positive interval over which the function repeats
B.
The greatest value attained by the function
C.
The time at which the function becomes zero
D.
The difference between the maximum and minimum values
Correct Answer:
The shortest positive interval over which the function repeats
Explanation:
The fundamental period is the smallest positive interval after which the function has the same values again.
8. For a periodic function y(t), which relation shows repetition after two periods?
A.
y(t + 2T) = y(t)
B.
y(t + 2T) = 2y(t)
C.
y(t + 2T) = y(t) + 2T
D.
y(t + 2T) = 0
Correct Answer:
y(t + 2T) = y(t)
Explanation:
If T is a period, the function also repeats after any whole-number multiple of T, including 2T.
9. If f(t + T) = f(t) for all t, then f(t + 3T) is equal to:
A.
f(t)
B.
3f(t)
C.
f(t) + 3T
D.
Zero
Correct Answer:
f(t)
Explanation:
A periodic function repeats after every whole-number multiple of its period, so f(t + 3T) equals f(t).
10. Which statement is necessary for a function to be periodic?
A.
Its values must repeat at equal intervals
B.
Its values must always increase
C.
Its values must always be positive
D.
Its graph must be a straight line
Correct Answer:
Its values must repeat at equal intervals
Explanation:
A periodic function is defined by the repetition of its values after a fixed positive interval.
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