Question

Which of the following systems of nonlinear inequalities is graphed below?

Answer 1

B.

Explanation:

The circle has center at (0, 0) and radius 3, so its equation is

x^2 + y^2 = 9

Since the shading is inside the circle, the inequality of the circle must be

x^2 + y^2 <= 9

This eliminates choices A. and C.

The parabola has its vertex at (-1, 1) and opens downward, so its equation is

y = -(x + 1)^2 + 1

Since the shading is below the parabola, its inequality is

y <= -(x + 1)^2 + 1

Answer: B.

Answer 2

B.

Explanation:

The easiest and quickest way to do this is to use common sense/guess and check on the graphing calc. We know from the circle graph that the inside is shaded, so the inequality must be ≤. That eliminates A and C as our answer choices. We are left with B and D. B is the correct choice because of the inequality ≤.