Answer :
Notice that:
[tex]\log _3x,[/tex]is well defined for x>0, therefore the domain of the given function is:
[tex](0,\infty).[/tex]Now, the range of the function is:
[tex](-\infty,\infty).[/tex]To find the x-intercept we set y(x)=0, and solve for x:
[tex]\begin{gathered} 0.7\log _3(x)=0, \\ \log _3(x)=0, \\ x=1. \end{gathered}[/tex]Therefore the x-intercept is at (1,0).
Now, to find the y-intercept we should evaluate the y at x=0, but the logarithm is undefined at x=0, therefore there is no y-intercept.
Finally, the function has an asymptote at x=0.
Answer:
Domain:
[tex](0,\infty).[/tex]Range:
[tex](-\infty,\infty).[/tex]x-intercept:
[tex](1,0)\text{.}[/tex]No y-intercept.
Asymptote:
[tex]x=0.[/tex]