#1
Which of the following functions is periodic?
f(x) = sin(x)
ExplanationSine function repeats its values at regular intervals.
#2
What is the period of the function f(x) = cos(2x)?
2π
ExplanationThe period of cosine function is 2π.
#3
What is the range of the function f(x) = sin(x)?
[-1, 1]
ExplanationThe range of sine function lies between -1 and 1.
#4
If f(x) = cos(x), then f(x + 2π) is equivalent to:
cos(x)
ExplanationAdding 2π to the argument doesn't change the value of cosine function.
#5
What is the period of the function f(x) = 2sin(3x)?
π/3
ExplanationThe period of sine function is 2π/n where n is the coefficient of x, hence π/3.
#6
Which of the following is NOT a periodic function?
f(x) = 1/x
ExplanationThe function 1/x does not repeat its values at regular intervals.
#7
The function f(x) = sin(x) has a period of:
2π
ExplanationSine function repeats its values every 2π.
#8
What is the amplitude of the function f(x) = 3sin(2x)?
3
ExplanationAmplitude represents the maximum displacement from the mean value which is 3 in this case.
#9
The period of the function f(x) = tan(x) is:
π/2
ExplanationThe period of tangent function is π/2.
#10
What is the phase shift of the function f(x) = cos(2x - π/4)?
π/4
ExplanationSubtracting π/4 from the argument shifts cosine function by π/4 to the right.
#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)
ExplanationAdding π/2 to the argument shifts cosine function by π/2 to the left.
#12
If f(x) = sin(x), what is f(x + π/2)?
cos(x)
ExplanationShifting the argument by π/2 changes sine function to cosine function.
#13
If f(x) = sin(x), what is f(x + π)?
-sin(x)
ExplanationAdding π to the argument changes sine function to its negative.
#14
What is the phase shift of the function f(x) = sin(3x + π/3)?
-π/3
ExplanationSubtracting π/3 from the argument shifts sine function by π/3 to the left.
#15
What is the phase shift of the function f(x) = sin(4x - π/2)?
π/8
ExplanationSubtracting π/2 from the argument shifts sine function by π/8 to the right.