Question

A function f is odd and f(x)=x^2 for all x>0. Sketch the graph of of this function and then write the rule of the function as a single formula
Pls solve I put 77 points ito this

Answer 1

The odd function is:

f(x) = sgn(x)*x^2

And the graph can be seen at the end.

How to get the formula of the function?

An odd function has the property:

f(-x) = -f(x).

In this case, for x > 0 we have:

f(x) = x^2

Notice that if we evaluate that in a negative number, we get:

f(-2) = (-2)^2 = 2^2 = f(2)

So, this is actually even.

To transform it into an odd function, we can multiply it by the sign function:

f(x) = sgn(x)*x^2

Now, when x is negative, the outcome will be negative, so the function is odd. The graph can be seen below.

If you want to learn more about odd functions:

brainly.com/question/2284364

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