Question

How to tell if a function is even or odd.

A) Symmetric with respect to the x-axis
B) Symmetric with respect to the y-axis
C) f(x)=f(−x) for even functions
D) f(x)=−f(−x) for odd functions

Answer 1

To determine if a function is even or odd, you can use the properties mentioned in options C and D. An even function is symmetric with respect to the y-axis, while an odd function is symmetric with respect to the origin.

Step-by-step explanation:

To determine whether a function is even or odd, you can use the properties mentioned in options C and D. An even function is symmetric with respect to the y-axis, which means that if you reflect the function across the y-axis, it remains unchanged (f(x) = f(-x)). On the other hand, an odd function is symmetric with respect to the origin, meaning that if you reflect the function across both the x-axis and the y-axis, it remains unchanged (f(x) = -f(-x)). So, to tell if a function is even, you would check if f(x) = f(-x), and to tell if it is odd, you would check if f(x) = -f(-x).