Question

consider f(x) = x^3 + x^1 would the function be even, odd, neither,or not enough information to determine

Answer 1

Answer:

The function is odd

Step-by-step explanation:

Even functions and odd functions are those which satisfy particular symmetry relations as follows:

f(x) is even if f(-x) = f(x)

f(x) is odd if f(-x) = -f(x)

Not all functions are eligible for being even or odd.

Considering

$f(x)=x^3+x^1$

Let's find f(-x)

$f(-x)=(-x)^3+(-x)^1$

Since $(-x)^3=(-x)(-x)(-x)=-x^3$

And $(-x)^1=-x:$

$f(-x)=-(x)^3-(x)^1$

Factoring by -1:

$f(-x)=-((x)^3+(x)^1)$

The expression in parentheses if f(x), thus:

$f(-x)=-f(x)$

And the function is odd.