Q. Function f is graphed.According to the graph, is f even, odd, or neither?Choose 1 answer:(A) Even(B) Odd(C) Neither
Definition of Even and Odd Functions: To determine if the function f is even, odd, or neither, we need to understand the definitions of even and odd functions.An even function satisfies the condition f(x)=f(−x) for all x in its domain, which means the graph of the function is symmetric with respect to the y-axis.An odd function satisfies the condition f(−x)=−f(x) for all x in its domain, which means the graph of the function is symmetric with respect to the origin.Without the actual graph, we cannot perform the visual check for symmetry. However, for the sake of this problem, let's assume we have the graph in front of us and we are checking for symmetry.
Symmetry Checks for Even Function: We look at the graph of function f and check for y-axis symmetry. If the graph looks the same on the left and right sides of the y-axis, then the function is even. We also check for origin symmetry. If rotating the graph 180 degrees around the origin results in the same graph, then the function is odd. If the graph does not exhibit either of these symmetries, then the function is neither even nor odd. Again, since we do not have the actual graph, we cannot perform these checks, but this is the process we would follow.
Symmetry Checks for Odd Function: Since we cannot visually inspect the graph, we cannot definitively determine whether the function f is even, odd, or neither. Therefore, we cannot provide a final answer without the graph.
More problems from Symmetry and periodicity of trigonometric functions