005 Sample Final A, Question 19

Question Consider the following function,

$f(x)=-\sin \left(3x+{\frac {\pi }{2}}\right)+1$

     a. What is the amplitude?
     b. What is the period?
     c. What is the phase shift?
     d. What is the vertical shift?
     e. Graph one cycle of f(x). Make sure to label five key points.

Final Answers
a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, $a_{n}=(-a)^{n}$
b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
c) False. $y=x^{2}$ does not have an inverse.
d) True. $cos^{2}(x)-cos(x)=0$ has multiple solutions.
e) True.
f) False.

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