Question

Give an example of an odd function and explain algebraically why it is odd. (3 points)

Answer 1

Answer: $f(x)=5x^{3}-x$

Step-by-step explanation:

1. By definition, algebraically, a function is odd when:

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

2. Therefore, if you have the following function:

$f(x)=5x^{3}-x$

You can know if it is odd by substituting $x=-x$:

$f(-x)=5(-x)^{3}-(-x)$

 $f(-x)=-5x^{3}+x$

3. $-f(x)$ is:

$-f(x)=-5x^{3}+x$

4. Then, as $-f(x)=f(-x)$ it is odd

Answer 2

Answer:

See below

Step-by-step explanation:

In an odd function f(-x) will equal -f(x).

An example is f(x) = x^3:-

f(-x) = (-x)^3 and -f(x)  = -x^3:-

(-x)^3 = -x * -x * -x = -x^3.