Trigonometry Graphing Trig Functions 2 — Questions and Answers
Question 1: What is the phase shift of y = sin(x − π/3)?
- π/3 to the left
- π/3 to the right (Correct answer)
- π/6 to the right
- π/3 upward
Correct answer: π/3 to the right
The phase shift is x − π/3 = 0 → x = π/3, shifting the graph π/3 units to the right.
Question 2: Which transformation does y = cos(x) + 3 represent?
- Horizontal shift right 3
- Vertical shift up 3 (Correct answer)
- Amplitude increase to 3
- Period reduced to 3
Correct answer: Vertical shift up 3
Adding 3 outside the cosine function shifts the entire graph up 3 units (vertical translation).
Question 3: What is the period of y = tan(2x)?
- π
- π/2 (Correct answer)
- 2π
- 4π
Correct answer: π/2
The period of tangent is π/|b|, so π/2 = π/2.
Question 4: What is the vertical asymptote nearest to x = 0 for y = tan(x)?
- x = 0
- x = π
- x = π/2 (Correct answer)
- x = π/4
Correct answer: x = π/2
Tangent is undefined when cos(x) = 0, which first occurs at x = π/2.
Question 5: The graph of y = −sin(x) is a reflection of y = sin(x) over which axis?
- y-axis
- x-axis (Correct answer)
- line y = x
- origin only
Correct answer: x-axis
Multiplying by −1 outside the function reflects the graph across the x-axis.
Question 6: What is the midline of y = 2cos(x) − 5?
- y = 2
- y = −5 (Correct answer)
- y = 0
- y = −3
Correct answer: y = −5
The midline is the vertical shift, given by the constant term outside: y = −5.
Question 7: How many complete cycles does y = sin(3x) complete on [0, 2π]?
- 1
- 2
- 3 (Correct answer)
- 6
Correct answer: 3
The period is 2π/3, so there are 2π ÷ (2π/3) = 3 complete cycles in [0, 2π].
Trigonometry Graphing Trig Functions 2
What is the phase shift of y = sin(x − π/3)?