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
1 answer:
The odd function is:
f(x) = sgn(x)*x^2
And the graph can be seen at the end.
<h3>How to get the formula of the function?</h3>
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:
#SPJ1
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