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Problem 9
Match each function with its graph in choices A–F.
y = tan (x - π )
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D. <IMAGE> E. <IMAGE> F. <IMAGE>
Problem 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 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 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 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 1
Fill in the blank(s) to correctly complete each sentence.
The graph of y = sin (x + π/4) is obtained by shifting the graph of y = sin x ______ unit(s) to the ________ (right/left).
Problem 2
Fill in the blank(s) to correctly complete each sentence.
The graph of y = cos (x - π/6) is obtained by shifting the graph of y = cos x ______ unit(s) to the ________ (right/left).
Problem 3
Fill in the blank(s) to correctly complete each sentence.
The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of ________.
Problem 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 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 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).
Problem 7
Fill in the blank(s) to correctly complete each sentence.
The graph of y = 3 + 5 cos (x + π/5) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)
Problem 8
Fill in the blank(s) to correctly complete each sentence.
The graph of y = -2 + 3 cos (x - π/6) is obtained by shifting the graph of y = cos x horizontally ________ unit(s) to the __________, (right/left) stretching it vertically by a factor of ________, and then shifting it vertically ________ unit(s) __________. (up/down)
Problem 9
Match each function with its graph in choices A–I. (One choice will not be used.)
y = sin (x - π/4)
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
G. <IMAGE> H. <IMAGE> I. <IMAGE>
Problem 11
Match each function with its graph in choices A–I. (One choice will not be used.)
y = cos (x - π/4)
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
G. <IMAGE> H. <IMAGE> I. <IMAGE>
Problem 16
Match each function with its graph in choices A–I. (One choice will not be used.)
y = -1 + cos x
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
G. <IMAGE> H. <IMAGE> I. <IMAGE>
Problem 19
Match each function in Column I with the appropriate description in Column II.
I
y = 3 sin(2x - 4)
II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3
Problem 21
Match each function in Column I with the appropriate description in Column II.
I
y = -4 sin(3x - 2)
II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3
Problem 25
Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.
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Problem 27
Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.
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Problem 29
Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.
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Problem 31
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin (x + π)
Problem 33
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = -¼ cos (½ x + π/2)
Problem 35
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 3 cos [π/2 (x - ½)]
Problem 37
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 - sin(3x - π/5)
Problem 39
Graph each function over a two-period interval.
y = cos (x - π/2 )
Problem 41
Graph each function over a two-period interval.
y = sin (x + π/4)
Problem 45
Graph each function over a one-period interval. See Example 3.
y = (3/2) sin [2(x + π/4)]
Problem 47
Graph each function over a one-period interval.
y = -4 sin(2x - π)
Problem 51
Graph each function over a two-period interval. See Example 4.
y = -3 + 2 sin x