precalculus
bdadio
precalc.docx1. How do you find the period of a cosine function of the form
y = cos bx?
The period of y = cos bx is
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2π |
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b |
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The period of y = cos bx is 2πb.
The period of y = cos bx is
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π |
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b |
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The period of y = cos bx is πb.
2. What is the amplitude of
y = 6 sin x?
3. Use the graph of the function to answer the following.
f(x) = cos x
on the interval [−2π, 2π]
(a) Find the x-intercepts of the graph of
y = f(x).
(Enter your answers as a comma-separated list.) x = (b) Find the y-intercepts of the graph of
y = f(x).
(Enter your answers as a comma-separated list.) y = (c) Find the intervals on which the graph of
y = f(x)
is increasing and the intervals on which the graph of
y = f(x)
is decreasing. (Enter your answers using interval notation.)
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increasing |
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decreasing |
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(d) Find the relative extrema of the graph of
y = f(x).
(Enter your answers as a comma-separated list of ordered pairs.)
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relative maxima |
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relative minima |
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4. Find the period and the amplitude.
y = 8 cos(3x)
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period |
= |
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amplitude |
= |
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5. Find the period and amplitude.
y = −4 sin
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x |
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3 |
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period |
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amplitude |
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6. Find the period and amplitude.
y =
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3 |
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2 |
cos
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πx |
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4 |
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period |
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amplitude |
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7. Find the period and amplitude.
y =
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3 |
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2 |
cos
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x |
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4 |
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(period) |
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(amplitude) |
8. Describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.
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f(x) |
= |
sin 2x |
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g(x) |
= |
sin(−2x) |
The graph of g is a vertical shift of the graph of f 2 units downward.The graph of g is a horizontal shift of the graph of f 2 units to the right. The graph of g is a vertical shift of the graph of f 2 units upward.The graph of g is a reflection of the graph of f in the y-axis.The graph of g is a horizontal shift of the graph of f 2 units to the left.
9. Describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.
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f(x) |
= |
cos 4x |
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g(x) |
= |
−3 + cos 4x |
The graph of g is a vertical shift of the graph of f 3 units downward.The graph of g is a reflection of the graph of f in the y-axis. The period of g is 3 that of f.The graph of g is a horizontal shift of the graph of f 3 units to the right.The graph of g has an amplitude 3 times that of the graph of f.
10 Sketch the graphs of f and g in the same coordinate plane. (Include two full periods.)
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f(x) |
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sin x |
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g(x) |
= |
sin
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11. Sketch the graph of the function by hand. Use a graphing utility to verify your sketch. (Include two full periods.)
f(x) = 3 cos (x + π/7)
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