Identify the odd function.(1 point)

Question

Responses

f(x)=2(x+1)3
f left parenthesis x right parenthesis equals 2 left parenthesis x plus 1 right parenthesis cubed

f(x)=x4
f left parenthesis x right parenthesis equals x superscript 4 baseline

f(x)=3x2
f left parenthesis x right parenthesis equals 3 x squared

f(x)=2x3

Answer 1

To identify the odd function from the given options, we can recall that a function \( f(x) \) is considered odd if it satisfies the condition \( f(-x) = -f(x) \) for all \( x \) in its domain.

Let's evaluate each function:

1. \( f(x) = 2(x+1)^3 \):

   • \( f(-x) = 2(-x + 1)^3 = 2(1 - x)^3 \) (which does not equal \(-f(x)\)).

2. \( f(x) = x^4 \):

   • \( f(-x) = (-x)^4 = x^4 \) (this is equal to \( f(x) \), so this function is even).

3. \( f(x) = 3x^2 \):

   • \( f(-x) = 3(-x)^2 = 3x^2 \) (this is equal to \( f(x) \), so this function is even).

4. \( f(x) = 2x^3 \):

   • \( f(-x) = 2(-x)^3 = -2x^3 = -f(x) \) (this satisfies the condition for odd functions).

Therefore, the odd function among the choices is:

f(x) = 2x^3.