Precalculus
posted by Elle on .
Given the following values for f(t):
t : f(t)
3 : 7
6 : 6
9 : 19
12 : 6
15 : 7
18 : 6
a) What is the period, frequency, midline, amplitude, maximum, and minimum?
b)Find a possible formula for f(t)
c)Find the domain and range of f(t)
d)Find a formula for an inverse function of f(t). (Hint: you will need to restrict the domain)What is the domain and range of the inverse function?

sketch it
It goes from 7 to 7, one period, in (153) = 12 second period
frequency = 1/period = 1/12
midline = (197)/2 = 6
single amplitude = 196 = 13 so double amplitude = 26
max = 19. min = 7
domain from 3 to 18 unless you let it go on the same shape from oo to +oo
range from 7 to + 19
There is no inverse function for the whole thing because there are multiple values of x for the same y in the original, therefore multiple values of y for the same x in the invers
Therefore you will have to split it up in the original to the section from x = 3 o 9, then from 9 to 15 , then from 15 to 18 and it is a nice straight line in each.