Answer
please see image
.
Work Step by Step
1. The inequality sign is $\geq $, so we draw a solid border
2. The border, $y=\log_{2}(\mathrm{x}+1)$
is a logarithmic function, base $2 > 1,$
It is obtained from $\log_{2}x$ by shifting left by one unit.
The function is defined only for $x>-1.$
This means that its vertical asymptote, $x=-1$
will not be included in the solution, and will be a border.
We graph it with a dashed line (not included).
Plot some points (see table)
and join with a smooth (solid) curve
3. We can't test the point $(0,0)$, as it lies on the border curve.
We test (1,0)
$ 0 \geq \log_{2}(1+1)\quad ?$
$0 \geq \log_{2}2\quad ?$
$0 \geq 1\quad ?$
No.
4. Shade the region that the point (1,0) does not belong to.
Also, apply the observation about the vertical asymptote
(we shade the region to the right of the asymptote)
