Answer
See the graph below:
Work Step by Step
Let us draw the graph of $ f\left( x \right)=\log x $ as follows:
Construct the table of coordinates for $ f\left( x \right)={{\log }}x $ and choose the appropriate values for $ x $ and calculate the corresponding $ y\text{-values}$.
Also, plot every point provided in the above table and join them using a smooth curve, and the $ y\text{-axis}$ or $ x=0$ is the vertical asymptote.
Now, the curve of $ g\left( x \right)=-\log \left( x+3 \right)$ is obtained by translating the graph of $ f\left( x \right)=\log x $ to the left by 3 units and then taking a reflection about the $ x\text{-axis}$.
So, the graph will be $ g\left( x \right)=-\log \left( x+3 \right)$ and we plot $ f\left( x \right)=\log x $ in the same rectangular plane.
In the above graph:
Vertical asymptote is $ x=0$
Domain is $\left( -\infty,0 \right)$
And the range is $\left( -\infty,\infty \right)$ of the function $ f\left( x \right)=\log x $
The vertical asymptote is $ x=0$,
Domain is $\left( -3,\infty \right)$
The range is $\left( -\infty,\infty \right)$ of the function $ g\left( x \right)=-\log \left( x+3 \right)$.
