Answer
The solution set is the region shaded GRAY
.
Work Step by Step
We will graph the solution region for each inequality.
Quadratic functions have a parabola for a graph.
To graph a line, we need two points...unless we know it is vertical or horizontal.
1. (red)
Border:$\quad y=x^{2}-1\quad $solid line ( sign is $\geq )$,
The curve is a parabola that opens up $(a=1>0)$ , with
vertex: $(0,-1)$
x-intercepts:
$0=x^{2}-1$
$0=(x+1)(x-1)$
x-intercepts:$ \quad \pm 1$
Testing $(0,0):\quad 0 \geq 0^{2}-1\quad?$
Yes, shade the region containing $(0,0)$
2 (blue)
$x-y=-1 \quad $solid line ( sign is $\geq )$,
x-intercept:$\quad x-0=-1\quad$ point: ($-1,0)$
y-intercept:$ \quad 0-y=-1\quad$ point: ($0,1)$
Testing $(0,0)$:$\quad 0-0 \geq -1 \quad ?$
Yes, shade the region containing (0,0)
The solution set is the region with BOTH shadings.
The solution set is the region shaded GRAY