Q 68. - Precalculus Enhanced with Graphing Utilities

Question

Match the graph with a logarithmic function :

The functions are :

$$\begin{gathered} A.y={\log }_{3}x \\ B.y={\log }_3(-x) \\ C.y=-{\log }_{3}x \\ D.y=-{\log }_3(-x) \\ E.y={\log }_{3}x-1 \\ F.y={\log }_3(x-1) \\ G.y={\log }_3(1-x) \\ H.y=1-{\log }_{3}x \end{gathered}$$

Step-by-Step Solution

Answer

The following graph matches with the function is : $H. y= 1-{\log }_{3}x$

Step 1. Given information

Given graph is :  

Step 2. Points on the curve

The points are :

$x$	$y=1-{\log }_{3}x$
$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$	$2$
$1$	$1$
$3$	$0$

Step 3. Graph of the function

The graph of the function $y=1-{\log }_{3}x$ is :