Solution assignment 05 Logarithmic functions and graphs

Sketch the graph of the following logarithmic function:

$y=2+\log[2(x+1)]$

The logarithm:

$\log[2(x+1)]$

is defined for:

$2(x+1)>0$

$x>-1$

and its graph intersects with the X-axis if:

$2(x+1)=1$

$x=-\displaystyle\frac{1}{2}$

We can verify the result in the figure.

The graph is only valid for $x>-1$ .