Understanding Periodic Functions Quiz

Test your understanding of periodic functions in trigonometry with this quiz featuring questions on periods, ranges, amplitudes, and phase shifts.

#1

Which of the following functions is periodic?

f(x) = x^2
f(x) = sin(x)
f(x) = e^x
f(x) = ln(x)
1 answered
#2

What is the period of the function f(x) = cos(2x)?

π
2π/3
π/2
1 answered
#3

What is the range of the function f(x) = sin(x)?

[-1, 1]
(0, ∞)
(-∞, 0)
(-1, 1)
1 answered
#4

If f(x) = cos(x), then f(x + 2π) is equivalent to:

f(x)
cos(x + 2π)
cos(x)
f(x + 2)
1 answered
#5

What is the period of the function f(x) = 2sin(3x)?

π/3
π
1 answered
#6

Which of the following is NOT a periodic function?

f(x) = cos(x)
f(x) = 1/x
f(x) = tan(x)
f(x) = sin(x)
#7

The function f(x) = sin(x) has a period of:

π
π/2
#8

What is the amplitude of the function f(x) = 3sin(2x)?

3
2
-3
-2
#9

The period of the function f(x) = tan(x) is:

π
π/2
None of the above
#10

What is the phase shift of the function f(x) = cos(2x - π/4)?

π/4
-π/4
π/2
-π/2
#11

Which of the following represents a phase shift of π/2 for the function f(x) = cos(x)?

f(x) = cos(x + π/2)
f(x) = cos(x - π/2)
f(x) = cos(x + π)
f(x) = cos(x - π)
#12

If f(x) = sin(x), what is f(x + π/2)?

cos(x)
-sin(x)
-cos(x)
sin(x)
#13

If f(x) = sin(x), what is f(x + π)?

-sin(x)
sin(x)
cos(x)
-cos(x)
#14

What is the phase shift of the function f(x) = sin(3x + π/3)?

-π/3
π/3
2π/3
-2π/3
#15

What is the phase shift of the function f(x) = sin(4x - π/2)?

π/8
-π/8
π/4
-π/4

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