Question

Suppose an exponential function can be written in the form y=ab^x, and we know the common ratio b and some point (ℎ,k). True or false: The function can also be written as y=k·b^x-h.

Answer 1

true

Explanation:

y = ab^x

the coordinates of the point are x and y values.

so, we can express "a" by these values :

k = ab^h

a = k/(b^h) = k × b^-h

now we use this identity in the original equation and get

y = k × b^-h × b^x = k×b^(x-h)

and that is exactly the same as the proposed form.