Which of the following could be the graph of y is equal to x to the n th power where n is even?
Answer
A
Image with description On a coordinate plane, x-axis is labeled with "x" ranges from negative 7 to 7 in increment of 1 and y-axis is labeled with "y" ranges from negative 7 to 7 in increment of 1. The curve with arrows at both ends, indicating it extends infinitely. On the left, it rises sharply from the lower part of the third quadrant near "negative 2 comma negative 7", curving upwards as it moves right. It passes through the point "negative 1 comma negative 1", then flattens significantly as it approaches the origin, crossing "0 comma 0" horizontally. Continuing to the right into the first quadrant, it passes through "1 comma 1" and then bends upwards, raising sharply toward the top of the grid near "2 comma 7".
B
Image with description On a coordinate plane, x-axis is labeled with "x" ranges from negative 7 to 7 in increment of 1 and y-axis is labeled with "y" ranges from negative 7 to 7 in increment of 1. The graph displays a symmetric, inverted u-shaped curve with arrows at both ends pointing downwards. Its highest point, or vertex, is located at the origin "0 comma 0". From the vertex, the curve slopes downward symmetrically to both the left and the right. It passes through the points "negative 1 comma negative 1" and "1 comma negative 1", extending downwards towards "y equals negative 7".
C
Image with description On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi in increment of pi and the y axis ranges from negative 1 to 7 in increment of 1. A central downward-opening parabolic branch has its local maximum vertex at "0 comma 2", with its arms extending vertically downward toward y equals negative 2. Two upward-opening parabolic branches sit above, each with a local minimum vertex at approximately "negative pi comma 4" and "pi comma 4", with their arms extending upwards toward y equals 6. Disconnected fractional vertical curve fragments with arrows are visible near the outer boundaries at x equals negative 2 pi and x equals 2 pi.
D
Image with description On a coordinate plane, x-axis is labeled with "x" ranges from negative 7 to 7 in increment of 1 and y-axis is labeled with "y" ranges from negative 7 to 7 in increment of 1. The curve with arrows at both ends, indicating it extends infinitely. On the left, it rises sharply from the upper part of the second quadrant near "negative 2 comma 7", curving downwards as it moves right. It passes through the point "negative 1 comma 1", then flattens significantly as it approaches the origin, crossing "0 comma 0" horizontally. Continuing to the right into the fourth quadrant, it passes through "1 comma negative 1" and then bends downward, dropping steeply toward the bottom of the grid near "2 comma negative 7".