Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passe

Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passes through the point P(1,4).


a. f(x)=-2(2^x)


b. f(x)=2(2^x) -2


c. f(x)=2(1.5^x)-2


d.f(x)=4(1.5^x)-2

Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passe
d


You're actually given too much information for this multiple choice question.


d is the only choice which passes through (1,4), for example.


4(1.5^1) - 2 = 4*1.5 - 2 = 6-2 = 4


y-intercept at 2 means the function passes through (0,2), and d is the only one that does this as well.


(b,c and d have horizontal asymptotes of y = -2)
Reply:f(0) = ba^0 + c = b + c = 2


f(1) = ba^1 + c = ab + c = 4


so ab - b = 2





since the horizontal asymptote is y = -2, we know ba^x, which has y=0 as horizontal asymptote, has been translated down 2, so c = -2.





then b - 2 = 2, b = 4, and


4a - 4 = 2


4a = 6


a = 1.5





so f(x) = 4(1.5^x) - 2, answer d.