Question

Use complete sentences to analyze the graph of the function f(x) = log (base 1/4) x
descrive teh domain, range and general shape of the graph

Answer 1

try to find the inverse function of it. then look of its Domain and Range.
Then (D->R,R->D) (f^-1->f)
Then the origenal function is a reflection along y=x. Then you can see how it looks.

Answer 2

i dont think thats right....

Answer 3

Do you how the inverse function is relating to a function?

Answer 4

I would plot a few key points to get the general shape.

\( log_{\frac{1}{4}}(x) =y \) corresponds to \( (\frac{1}{4})^y = x \)
we know that no matter what power we choose 1/4 will not be negative, so x>0
\( (\frac{1}{4})^{1} = \frac{1}{4} \) so \( log_{\frac{1}{4}}(\frac{1}{4}) =1 \)
\( (\frac{1}{4})^{0} = 1 \) so \( log_{\frac{1}{4}}(1) =0 \)
\( (\frac{1}{4})^{-1} = 4 \) so \( log_{\frac{1}{4}}(4) = -1 \)

sketch the graph

you can see the domain is (0, inf)
and though it is slowly going down, it can reach any negative number, so its
range is (-inf, inf)