Question

the graph shows a function. is the function even, odd, or neither? use the drop - down menus to explain.
click the arrows to choose an answer from each menu.
for the function on the graph, opposite x - values have choose... y -
values. this shows the function is choose... because its graph has
choose...

Explanation:

An odd function has the property that \(f(-x)=-f(x)\) for all \(x\) in its domain. This means that the graph of an odd function is symmetric about the origin. If we take a point \((x,y)\) on the graph of an odd function, then the point \((-x, -y)\) is also on the graph. Looking at the given graph, for opposite \(x -\)values (e.g., if \(x = 1\) and \(x=- 1\)), the \(y -\)values are also opposites.

Answer:

For the function on the graph, opposite \(x -\)values have opposite \(y -\)values. This shows the function is odd because its graph has symmetry about the origin.