Trigonometry Graphing Trig Functions 3 β Questions and Answers
Question 1: What is the range of y = 4sin(x) β 1?
- [β4, 4]
- [β5, 3] (Correct answer)
- [β1, 4]
- [β3, 5]
Correct answer: [β5, 3]
Amplitude 4 gives [β4, 4] for the base, then shifting down 1 gives [β5, 3].
Question 2: Which equation has a graph with amplitude 3 and period Ο?
- y = 3sin(x)
- y = 3sin(2x) (Correct answer)
- y = 3sin(Οx)
- y = sin(3x)
Correct answer: y = 3sin(2x)
Amplitude = 3 and period = 2Ο/2 = Ο, matching y = 3sin(2x).
Question 3: For y = cos(x β Ο/2), which familiar function does it equal?
- βsin(x)
- sin(x) (Correct answer)
- βcos(x)
- tan(x)
Correct answer: sin(x)
cos(x β Ο/2) = sin(x) by the co-function shift identity.
Question 4: What is the x-intercept of y = sin(x) closest to x = Ο/2 (other than Ο/2 itself)?
- x = 0
- x = Ο (Correct answer)
- x = 3Ο/2
- x = 2Ο
Correct answer: x = Ο
The next x-intercept after Ο/2 is at x = Ο where sin(Ο) = 0.
Question 5: What does stretching y = sin(x) horizontally by a factor of 2 produce?
- y = sin(2x)
- y = 2sin(x)
- y = sin(x/2) (Correct answer)
- y = sin(x) + 2
Correct answer: y = sin(x/2)
A horizontal stretch by factor 2 replaces x with x/2, giving y = sin(x/2).
Question 6: On what interval is y = cos(x) decreasing on [0, 2Ο]?
- (0, Ο/2)
- (Ο/2, 3Ο/2)
- (0, Ο) (Correct answer)
- (Ο, 2Ο)
Correct answer: (0, Ο)
cos(x) decreases from its maximum at x = 0 to its minimum at x = Ο, so on (0, Ο).
Question 7: What is the maximum value of y = β3cos(x) + 2?
- 5 (Correct answer)
- β1
- 3
- 2
Correct answer: 5
β3cos(x) ranges from β3 to 3, so β3cos(x) + 2 reaches a maximum of 3 + 2 = 5.
Trigonometry Graphing Trig Functions 3
What is the range of y = 4sin(x) β 1?