Question

Determine the following of the function y = 0.7log3(x) Domain • Range X-intercept Y-intercept Asymptote

Answer 1

Notice that:

`\log _3x,`

is well defined for x>0, therefore the domain of the given function is:

`(0,\infty).`

Now, the range of the function is:

`(-\infty,\infty).`

To find the x-intercept we set y(x)=0, and solve for x:

`\begin{gathered} 0.7\log _3(x)=0, \\ \log _3(x)=0, \\ x=1. \end{gathered}`

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:

`(0,\infty).`

Range:

`(-\infty,\infty).`

x-intercept:

`(1,0)\text{.}`

No y-intercept.

Asymptote:

`x=0.`