Functional Analysis
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Unannounced Quiz Section 4.4-4.5
I.
Name___________________
Date_________ Period____
Short answer. Take your time when answering these questions.
1.__________________What is the period of the function y = –3cos

(x – 4) + 1 ?
5
2.__________________What is maximum value of the function y = 2sin
2
(x + 1) + 5?
3
3.__________________The phase shift for the sine function can be found by choosing the
x-coordinate of any
????
where the function is increasing.
4.__________________Find two different values of c (the phase shift) that could be used when
writing an equation of the curve below using cosine.
5.
Sine looks like the curve on the left. Sketch over the top of it
the cosine curve from 0 to 2.
6. Write the equation of the given graph …
________________ … using sine.
________________ … using -sine.
________________ … using cosine.
________________ … using -cosine.
II.
8.
Free Response. Graph at least one cycle of each of the following. Please sketch each
function clearly and neatly label all axes and asymptotes. Then, state the domain and range.
1

y = 3cos   x     1 .
3

Domain:
_________
Range:
_________
9.
y = tan x + 3
Domain:
_________
Range:
_________
10.
y = 4csc
2
x +1
5
Domain:
_________
Range
_________