Posted by tamara on .
By what fraction of the period of f(x)=10 cos(7 x) has the graph of f(x) been shifted to obtain the graph of g(x)=10 cos(7x pi/2). how do I approach this and solve for the fraction shift and the domain and range?

trig 
Damon,
2 pi is a whole circle or period
pi/2 is a quarter of a circle or period
the domain of this function is all real x, in other words x can be any real number positive or negative
However cosine is between 1 and +1 so range is between 10 and +10 
trig 
Reiny,
the period of y = 10cos(7x) is 2π/7
rewriting the second as
y = 10cos 7(x  π/14) we can see that the phase shift was
π/14 to the right.
so what fraction is that phase shift of the period?
(π/14)/(2π/7)
or
1/4 of the phase shift. 
trig 
Damon,
humm, looks like we agree in the end :)

Damon  trig 
Reiny,
Damon, when I opened the page and started to answer this question, I left it alone to watch the end of the WorldCup football game, and when I resumed I did not refresh the page, thus did not see your answer was already posted.