Question

Which statement best describes how to determine whether f(x) = x3 + 5x + 1 is an even function?

Answer 1

The answer is B) Determine whether (–x)^3 + 5(–x) + 1 is equivalent to x^3 + 5x + 1

Answer 2

Let f(x) be the real value function. Remember that: 
→ Even: f(x) = f(-x) → Odd: -f(x) = f(-x) 
If -f(x), then -f(x) = -x³ + 5x If x = -x, then f(-x) = -x³ + 5x 
Since -f(x) = f(x), the function is therefore odd.