6

Set 12: Linear Inequalities

Explanation

Answer: A

Solve the system: y>x2y > x^2 and y<4y < 4. (Non-linear preview)

A.

Region between the parabola y=x2y=x^2 and line y=4y=4

✓ Correct
B.

Region outside the parabola y=x2y=x^2 and below y=4y=4

C.

Region above y=4y=4 and inside parabola

D.

No solution

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Visualize the regions. 1. y>x2y > x^2: Region "inside" or above the parabola opening up. 2. y<4y < 4: Region below the horizontal line y=4y=4. 3. Intersection: The bowl-shaped region bounded below by the parabola and above by the line. Strategic Tip: y>f(x)y > f(x) is above the graph, y<f(x)y < f(x) is below. Choice B is incorrect because outside/below the parabola is y<x2y < x^2. Choice C is incorrect because above y=4y=4 is y>4y > 4. Choice D is incorrect because the regions clearly overlap (e.g., point (0,1)(0, 1) works).

Key Steps:

The correct answer is Region between the parabola y=x2y=x^2 and line y=4y=4

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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