Question

Can someone check. I got even because the origin is on the y axis

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Answer 1

Even means that the left side of the y-axis is an EXACT mirror image of the right side of the y-axis.
Is this what you see.

Answer 2

in mathematical terms you have symmetry of the graph about the y-axis.

Answer 3

The segment coming off the origin is shorter on the right side of the y axis, so it's not an exact mirror image?

Answer 4

that's right. It's not exact so it will not be even

Answer 5

Thank. Can you explain odd and neither please.

Answer 6

sure odd function implies that the function has symmetry about the origin. This is more trickier to explain.

It does follow this rule

\[f(-x) = -f(x)\]

Example:

You see that the function f, given by f(x) = x^3 is odd as when you when you rotate the graph about the y axis and then flip it upside down, you get the original graph.

Answer 7

In summary

EVEN function - symmetry about y -axis (turning the graph around the y axis makes the same graph again)
\[f(-x) = f(x)\]

ODD function - symmetry about origin (turning the graph about the y axis, and then flipping it upside down makes the same graph)
\[f(-x) = -f(x)\]

If the above rules don't apply, we say the graph is neither even nor odd.

Answer 8

So if you get such a question the best way to do this is either
1) Look at the graphs for symmetries discussed
2) If you are only given an equation:

Find f(-x) by replacing x with - x in the function's equation.
Then see if f(-x) is equivalent to either f(x) --> even or -f(x) --> odd.
Otherwise, neither.

Answer 9

Thank you very much. Im guessing the graph i posted is neither because it has neither symmetry on either axis?

Answer 10

that's right. If it was odd it look like this