Determine algebraically whether or not the function f(×)=-×^3-2×^2+5 is even or odd, and justify your answer.

Question

a. The function is odd because f(-×)=-f(×)
b. The function is odd because f(-×)=f(×)
c. The function is even because f(-×)=-f(×)
d. The function is even because f(-×)=f(×)
e. The function is neither even nor odd because f (-×)=f (×) and f (-×) = -f (×)

Answer 1

The correct answer is c. The function is even because f(-×)=-f(×).

To determine whether a function is even or odd, we need to analyze the function's symmetry behavior.

A function is even if it satisfies the condition f(-×)=f(×), meaning that if we substitute -× into the function, we get the same result as when we substitute × into the function. In this case, f(-×)= -(-×)^3 -2(-×)^2 + 5 = -(-×^3) -2×^2 + 5 = ×^3 - 2×^2 + 5.

A function is odd if it satisfies the condition f(-×)=-f(×), meaning that if we substitute -× into the function, we get the negative of the result when we substitute × into the function. However, in this case, f(-×) is not equal to -f(×).

Since the function satisfies the condition f(-×)=-f(×), we can conclude that the function is even.