Question

Which of the following is an odd function?(1 point)
Responses

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

f(x)=4x2
f left parenthesis x right parenthesis equals 4 x squared

f(x)=3x4
f left parenthesis x right parenthesis equals 3 x superscript 4 baseline

f(x)=4x3

Answer 1

To determine which of the functions is an odd function, we need to use the definition of an odd function. A function \( f(x) \) is considered odd if \( f(-x) = -f(x) \) for all \( x \).

Let's evaluate each function:

1. **\( f(x) = (x + 2)^3 \)**
\[
f(-x) = (-x + 2)^3 = -(x - 2)^3 \neq -f(x)
\]
(Not an odd function)

2. **\( f(x) = 4x^2 \)**
\[
f(-x) = 4(-x)^2 = 4x^2 = f(x)
\]
(Even function)

3. **\( f(x) = 3x^4 \)**
\[
f(-x) = 3(-x)^4 = 3x^4 = f(x)
\]
(Even function)

4. **\( f(x) = 4x^3 \)**
\[
f(-x) = 4(-x)^3 = -4x^3 = -f(x)
\]
(Odd function)

Based on this analysis, the function that is an odd function is:

**\( f(x) = 4x^3 \)**.