Question

How do you describe the transformation in `y=2^(x-3)`?

Answer 1

The form is `y=a b^x`, with #a = 1/8 and b = 2. The plot of {(x, Y)}, with Y = log y, on a semi-log graph paper will be a straight line,.

Explanation:

This is an exponential transformation, of the form `y=a b^x`.

A short Table for making the graph for

`y=2^(x-3)=(1/8)(2^x)`

is given below.

`(x, y): ... (-4,1/128) (-3, 1/64) (-2, 1/32) (-1, 1/16)`

`(0, 1/8) (1, 1/4) (2, 1/2) (3, 1) (4, 2)....(N, 2^(N-3)) ...`

Equating logarithms, `Y=log y =x log 2 - 3 log 2`

The plot of [{x, Y)}, with Y= log y, on a semi-log graph paper, will be a

straight line.