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Problem 4.37
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 - sin(3x - π/5)
Problem 4.38
Consider the function g(x) = -2 csc (4x + π). What is the domain of g? What is its range?
Problem 4.39
Graph each function over a two-period interval.
y = cos (x - π/2 )
Problem 4.39
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)
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Problem 4.39
Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = π sin πx
Problem 4.4
Fill in the blank(s) to correctly complete each sentence.
The graph of y = -3 sin x is obtained by stretching the graph of y = sin x by a factor of ________ and reflecting across the ________-axis.
Problem 4.40
Graph each function over a one-period interval.
y = -½ cos (πx - π)
Problem 4.41
Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.
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Problem 4.41
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)
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Problem 4.41
Graph each function over a two-period interval.
y = sin (x + π/4)
Problem 4.42
Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.
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Problem 4.43
A rotating beacon is located at point A, 4 m from a wall. The distance a is given by
a = 4 |sec 2πt|,
where t is time in seconds since the beacon started rotating. Find the value of a for each time t. Round to the nearest tenth if applicable.
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t = 1.24
Problem 4.43
Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.
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Problem 4.43
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)
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Problem 4.43
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts.
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Problem 4.44
Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.
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Problem 4.44
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts.
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Problem 4.45
Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.
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Problem 4.45
Graph each function over a one-period interval. See Example 3.
y = (3/2) sin [2(x + π/4)]
Problem 4.46
Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.
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Problem 4.47
Graph each function over a one-period interval.
y = -4 sin(2x - π)
Problem 4.5
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 2x
Problem 4.5
Fill in the blank(s) to correctly complete each sentence.
The graph of y = 6 + 3 sin x is obtained by shifting the graph of y = 3 sin x ________ unit(s) __________ (up/down).
Problem 4.51
Graph each function over a two-period interval. See Example 4.
y = -3 + 2 sin x
Problem 4.53
Graph each function over a two-period interval. See Example 4.
y = -1 - 2 cos 5x
Problem 4.55
Graph each function over a two-period interval.
y = 1 - 2 cos ((1/2)x)
Problem 4.57
Graph each function over a two-period interval.
y = -2 + (1/2) sin 3x
Problem 4.59
Consider the following function from Example 5. Work these exercises in order.
y = -2 - cot (x - π/4)
Based on the answer in Exercise 58 and the fact that the cotangent function has period π, give the general form of the equations of the asymptotes of the graph of y = -2 - cot (x - π/4).
Let n represent any integer.
Problem 4.6
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = tan 3x
Problem 4.6
Fill in the blank(s) to correctly complete each sentence.
The graph of y = -5 + 2 cos x is obtained by shifting the graph of y = 2 cos x ________ unit(s) __________ (up/down).