If f of x is an even function and open paren 6 comma 8 close paren is one the points on the graph of f of x , which reason explains why open paren negative 6 comma 8 close paren must also be a point on the graph?
Answer
A
The graph has rotational symmetry, so the point will be reflected across the y -axis.
B
The graph has rotational symmetry, so the point will be rotated 90 degrees about the origin.
C
Since the function is even, the outputs of a negative x -value and a positive x -value are the same.
D
Since the function is even, the outputs of a negative y -value and a positive y -value are the same.
Explanation
An even function satisfies f(-x) = f(x). Since f(6) = 8, it follows that f(-6) = 8, so (-6, 8) is also on the graph. This is why the outputs for opposite x-values are the same.
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