a function g can be represented with a graph that contains (-2,1) and (1, 1/64) . write an equation of the form g(x)=a x b^x to define the function.

Answer 1

(-2,1), (1, 1/64)

f(x) =ab^x is an exponential function

1=ab^-2 = a/b^2, a = b^2

1/64 = ab^1 = ab

a= 1/64b

b^2 = 1/64b

b^3 = 1/64

b = 1/4

a=(1/4)^2 = 1/16

g(x) = (1/16)(1/4)^x = (1/4)^2(1/4)^x

g(x) = (1/4)^(x+2) = (.25)^(x+2)

g(x) = (0.25)^(x+2)