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]

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