The asymptote is ![x=-3](https://tex.z-dn.net/?f=x%3D-3)
Domain is ![(-3, \infty)](https://tex.z-dn.net/?f=%28-3%2C%20%5Cinfty%29)
Range is ![(-\infty, \infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20%5Cinfty%29)
Explanation:
Given that the function is ![y=\log _{3}(x+3)](https://tex.z-dn.net/?f=y%3D%5Clog%20_%7B3%7D%28x%2B3%29)
<u>Asymptote:</u>
The function has no horizontal asymptote.
The given function is of the form,
has a vertical asymptote ![x=-h](https://tex.z-dn.net/?f=x%3D-h)
where ![h=3](https://tex.z-dn.net/?f=h%3D3)
Thus, the vertical asymptote is ![x=-3](https://tex.z-dn.net/?f=x%3D-3)
<u>Domain:</u>
The domain of the function is the set of all independent x - values for which the function is real and well defined.
Let us find the positive values for log
Thus, we have,
![x+3>0](https://tex.z-dn.net/?f=x%2B3%3E0)
![x>-3](https://tex.z-dn.net/?f=x%3E-3)
Thus, the function domain in interval notation is ![(-3, \infty)](https://tex.z-dn.net/?f=%28-3%2C%20%5Cinfty%29)
<u>Range:</u>
The range of the function is the set of all dependent y - values of the function.
Hence, the range of the function is ![(-\infty, \infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20%5Cinfty%29)