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Pre-calculus

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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?

  • Pre-calculus -

    sketch it
    It goes from -7 to -7, one period, in (15-3) = 12 second period
    frequency = 1/period = 1/12
    midline = (19-7)/2 = 6
    single amplitude = 19-6 = 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.

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