Question

Confusion about transformation: Why do y=3^-x and y= (1/3 )^x have the same curve?

Answer 1

Exponent rules. \(3^{-x} = \dfrac{1}{3^{x}} = \left(\dfrac{1}{3}\right)^{x}\)

Many times, the answer is not obvious. A little exploration is required.

Answer 2

\(y=3^{-x}\)
\(\ln y=-x \ln 3\)

different system
\( y'= (1/3 )^{x'} \)
\(\ln y'= x' ln (1/3 ) = - x' \ln (3 )\)

wot he said :)

Answer 3

Thank you both of you !!!