Checkpoint: Graphing Logarithmic Functions without Technology Solution

Graph the inverse of the given equation without technology.

$f (x) = {(\frac{2}{3})}^{- x}$

$f (x) = {(\frac{3}{2})}^{x}, f^{- 1} (x) = \log_{\frac{3}{2}} x$

Note

Q: What is the asymptote for the inverse function?
A: x = 0

Q: What is the domain and range of the inverse function?
A: The domain is $x > 0,$ and the range is all real numbers.