79.8k views
1 vote
Determine whether the function is even, odd, or neither. Verify the answer using a graphing utility !g(x)=x^3-5

1 Answer

2 votes

A function g(x) is even if g(x) = g(-x) for all values of x in the domain of the function.

Also, the function is odd if g(x) = -g(-x) for all values of x in the domain of the function.

The function f(x) = x³, for example, is odd, since

f(x) = x³ = x * x * x = (-1) * (-1) x * x * x * (-1) * (-1)= - (-x)(-x)(-x) = -f(-x)

Notice that we can multiply by (-1)*(-1) since it is equal to 1 and doesn't change the other factors.

Nevertheless, the given function x³ - 5, is not odd neither even. Let's take x = 1:

f(1) = 1³ - 5 = 1 - 5 = -4

f(-1) = (-1)³ - 5 = -1 - 5 = -6

So, f(-1) ≠ f(1) and f(-1) ≠ -f(1).

Graphing this function, we can check that this function isn't even nor odd:

User Mparaz
by
6.9k points