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Problem 4.61
Graph each function over a two-period interval.
y = sin [2(x + π/4) ] + 1/2
Problem 4.61
Consider the following function from Example 5. Work these exercises in order.
y = -2 - cot (x - π/4)
Use the fact that the period of this function is π to find the next positive x-intercept. Round to the nearest hundredth.
Problem 4.7
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = -½ cos 3x
Problem 4.7
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 4.8
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 5x
Problem 4.8
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 4.9
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 4.9
Match each function with its graph in choices A - D.
y = sec (x - π/2)
Problem 4.9
Match each function with its graph in choices A–F.
y = tan (x - π )
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
Problem 4.9
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 1 + 2 sin ¼ x