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

User Dave Costa
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1 Answer

14 votes

Answer:


f(x) =(x^3)/(|x|)

Explanation:

Being an odd function means that
f(-x) = -f(x).

Graphically, it means the function will be symmetric across the origin.

So, the graph will have to look like the shown graph.

This graph looks quite similar to the graph
f(x) = x^3, so we can use that as our parent function.

To get the graph to equal
x^2 for x>0, we must divide
x^3 by x.

However, this will simply result in the function
f(x) = x^2.

If we divide by the absolute value of x however, the graph will look as desired.

A function f is odd and f(x)=x^2 for all x>0. Sketch the graph of this function-example-1
User Regine
by
7.7k points

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