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Q1. Which of the following represents the phase shift of the function y = sin(x - π/4)?
Solution:
The phase shift of y = sin(x - C) is C. Here, C = π/4, so the phase shift is π/4 to the right.
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Q2. What is the period of the function y = sin(x)?
Solution:
The period of the sine function is 2π.
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Q3. At what value of x does the function y = tan(x) have a vertical asymptote?
Solution:
The tangent function has vertical asymptotes at x = π/2 + nπ, where n is an integer. The first asymptote in [0, π] is at π/2.
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Q4. What is the maximum value of y = -2cos(x)?
Solution:
The maximum value occurs when cos(x) = -1, giving a maximum of -2 * -1 = 2.
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Q5. What is the x-intercept of the function y = cos(x) in the interval [0, 2π]?
Solution:
The cosine function equals zero at x = π/2 and x = 3π/2. The x-intercepts in [0, 2π] are π/2 and 3π/2.
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Q6. What is the period of the sine function?
Solution:
The period of the sine function is 2π, meaning it repeats every 2π units.
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Q7. What is the frequency of the function y = sin(2x)?
Solution:
The frequency of y = sin(Bx) is |B|/(2π). Here, B = 2, so the frequency is 2/(2π) = 1/π.
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Q8. What is the vertical asymptote of y = tan(x)?
Solution:
The vertical asymptotes of the tangent function occur at x = π/2 + nπ, where n is an integer.
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Q9. What is the phase shift of y = 4sin(2x + π)?
Solution:
The phase shift is found by setting 2x + π = 0, leading to a shift of -π/2.
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Q10. Which of the following is the correct phase shift of y = sin(x - π/4)?
Solution:
The phase shift is found by setting the inside of the sine function to zero, giving a shift of π/4 to the right.
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