1. Determine whether the function shown is even, odd, or neither. Provide an argument to explain your answer.
A. The function is odd because f(−x)=−f(x) .
B. The function is even because f(−x)=f(x) .
C. The function is both even and odd because f(−x)=−f(x) and f(−x)=f(x) .
D. The function is neither even nor odd because f(−x)≠−f(x) and f(−x)≠f(x) .
The correct answer is B. The function is even because when you substitute -x into the function, you get the same result as when you substitute x into the function.
An even function is symmetric with respect to the y-axis, meaning that if you reflect the graph across the y-axis, it remains unchanged. This symmetry is defined mathematically as f(-x) = f(x). In this case, the function satisfies this condition, making it an even function.