Answer
$\quad H(x)=1-\log_{3}x $.
Work Step by Step
We first locate the graph of $ f(x)=\log_{3}x $ among the six given graphs (from 47-52).
The graph of $ f(x)=\log_{3}x $
- nears the negative y axis as x approaches 0 from the right (graphs 49, 52),
- constantly rises, and passes through (1,0), (3,1), (9,2) (which is graph 52)
The graph 52 is the graph of $ f(x)=\log_{3}x $.
This graph (graph 47) is obtained from the graph of $ f(x)$ by:
- reflecting about the x axis: $-f(x)$
- and raising it up by 1 unit: $-f(x)+1=1-\log_{3}x $
which is $H(x)=1-\log_{3}x $.
