Answer:
Option C.
Step-by-step explanation:
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through the points (1,0) and (0,-2). So, the equation of line is
[tex]y-0=\frac{-2-0}{0-1}(x-1)[/tex]
[tex]y=2(x-1)[/tex]
[tex]y=2x-2[/tex]
It is a solid line and the shaded region lies below the line, so the sign of inequality must be "≤".
First inequality is [tex]y\leq 2x-2[/tex].
The parabola intersect the x-axis at 0 and 3, so the equation of of parabola is
[tex]y=(x-0)(x-3)[/tex]
[tex]y=x(x-3)[/tex]
[tex]y=x^2-3x[/tex]
It is a solid curve and the shaded region lies above the curve, so the sign of inequality must be "≥".
Second inequality is [tex]y\geq x^2-3x[/tex].
Therefore, the correct option is C.
