Show that any function of the form gx xyah can be written i

Show that any function of the form g(x) = xy^a-h can be written in the form g(x) = xy^a and can g(x) = xy^a-h + k be seen as a function that grows by equal multiplies over equal intervals?

Solution

g(x) = xy^a-h

=> g(x) = xy^a/y^h

=> g(x) = Cxy^a (Because 1/y^h is a constant for g(x))

=> g(x) = xy^a (Because Cy^a is again a constant and so Ccan be accomodated in y^a)

Consider g(x) = xy^a-h + k

g(0) = 0+k =k

g(1) = y^a-h+k

g(2) = 2y^a-h+k

g(3) = 3y^a-h + k

Now g(1) - g(0) = y^a-h

g(2)-g(1) = y^a-h

g(3)-g(2) = y^a-h

Hence g(x) is growing by factor of y^a-h over intervals of length 1

So yes g(x) can be seen as a function that grows by equal multiplies over equal intervals