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# Even and odd functions: Tables

Even functions are symmetrical about the y-axis: f(x)=f(-x). Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x). Let's use these definitions to determine if a function given as a table is even, odd, or neither.

## Want to join the conversation?

• How many points we should examine to be sure if a function is odd or even ?
• In the questions with the table you should just check every value given.
On graphs you can eyeball it.
If you're just given a function you input a -x and see what happens.

So for example you have f(x) = 4x^2 + 3
f(-x) = 4(-x)^2 + 3 = 4(x)^2 + 3 = f(x)
which means the function is even.
On the other hand g(x) = 3x + 2
g(-x) = 3(-x) + 2 = -3x + 2
so g(x) is not even, because f(-x) != f(x).

For odd functions it works the same.
h(x) = x^3 - x
h(-x) = (-x)^3 - (-x) = -x^3 + x = - (x^3 - x) = -h(x)
So h(x) is odd.
• I hate this
• I always visualize it in my mind. Also sobe subjects might take time to comprehend, try to be patient, use different sources.
• How can I find out if the graph is even or odd when there aren't any points that line up?
• Can you post a video explaining the hardest question in this unit