The graph of the function
[tex]y=-\log _3x[/tex]
is shown below:
The domain is the set of allowed x values of the function.
The range is the set of allowed y values of the function.
If you look at the graph, the domain is x greater than 0 towards infinity. We can write it as:
[tex]DOMAIN=(0,\infty)[/tex]
Then, take a look at this other version of the graph, zoomed in:
From this, we can clearly see that the range is y greater than -3 towards infinity. Thus, the range can be written as:
[tex]\text{RANGE}=(-3,\infty)[/tex]
An asymptote is a line the graph gets closer and closer to but never touches it.
If we look at the graph, we see that the y-axis (x = 0 ) is an asymptote and the line y = -3 is another asymptote, so,
[tex]\begin{gathered} \text{ASYMPTOTE} \\ y=-3 \\ x=0 \end{gathered}[/tex]Answers[tex]\begin{gathered} \text{Domain}=(0,\infty) \\ \text{Range}=(-3,\infty) \\ \text{Asymptote(s)}= \\ y=-3,x=0 \end{gathered}[/tex]
