We will see that we have a piecewise function:
- f(x) = x^2 for x > 0.
- f(x) = -x^2 for x ≤ 0.
The graph can be seen at the end.
What is an odd function?
A function is odd when f(-x) = -f(x) for all the values of x in the domain of the function.
In this case, we know that:
f(x) = x^2 for x > 0.
Then, for the negative range, the sign must change (but the quadratic function is even). Then we define the function in the negative range as:
f(x) = -x^2 for x ≤ 0.
This is the odd function (a piecewise function) for the whole domain:
- f(x) = x^2 for x > 0.
- f(x) = -x^2 for x ≤ 0.
The graph of the piecewise function can be seen below.
If you want to learn more about piecewise functions, you can read:
https://brainly.com/question/3628123
