Which graph represents the solution to the system of inequalities? x squared minus 4 y squared is less than 16; y is less than 2 to the x-th power
Answer
A
Image with description On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything above the curve and inside of the ellipse is shaded.
B
Image with description On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything below the curve and inside of the ellipse is shaded.
C
Image with description On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). A parabola opens to the right and goes through (9, 4), has vertex (4, 0), and goes through (9, negative 4). Another parabola opens to the left and goes through (negative 9, 4), has vertex (negative 4, 0), and goes through (negative 9, negative 4). Everything outside of the parabola and above the curve is shaded.
D
Image with description A left-opening dashed parabola has a vertex at left-parenthesis 0 comma negative 4 right-parenthesis and passes through left-parenthesis negative 6 comma 2 right-parenthesis and left-parenthesis negative 6 comma negative 2 right-parenthesis. A right-opening dashed parabola has a vertex at left-parenthesis 0 comma 4 right-parenthesis and passes through left-parenthesis 6 comma 2 right-parenthesis and left-parenthesis 6 comma negative 2 right-parenthesis. A dashed curve extends along the horizontal axis from left-parenthesis negative 10 comma 0 right-parenthesis to left-parenthesis negative 2 comma 0 right-parenthesis and then rises through left-parenthesis 0 comma 1 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The region outside the parabolas and below the curve is shaded one color. The region outside the parabolas and above the curve is shaded a second color. The region inside the parabolas and below the curve is shaded a third color.