Question

If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (–6, 8) must also be a point on the graph?
A. Since the function is even, the output of a negative x-value and its opposite is the same.
B. Since the function is even, the output of a negative y-value and its opposite is the same.
C. The graph has rotational symmetry, so the point will be reflected across the y-axis.
D. The graph has rotational symmetry, so the point will be rotated 90 degrees about the origin.

Answer 1

Since the function is even the outputs of a negative x-value and positive x-value are the same.

Answer 2

Definition: A function is "even" when f(x) = f(−x) for all x.

Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis.

If point (6, 8) is one the points on the graph of f(x), then f(6)=8 and since function is even, you can state that f(-6)=f(6)=8. This means that point (-6,8) must also be a point on the graph. Geometrically it means that the output of a negative x-value and its opposite is the same.

Answer: correct choice is A.