10/3/22 - Even & Odd Functions Flashcards
1
Q
How is an even function defined?
A
A function is even if f(x) = f(-x)
2
Q
How is an odd function defined?
A
A function is odd if -f(x) = f(-x)
3
Q
What can we tell about the graph of an even function?
A
It is symmetrical about the y-axis.
4
Q
What can we tell about the graph of an odd function?
A
It has 180 degree rotational symmetry about the origin.
5
Q
What coordinate pair does every odd function share?
A
(0, 0)
6
Q
If f(x) = x^p, then
f(x) is even when p is ____
and f(x) is odd when p is ____
A
Even, odd
7
Q
How do you find the parity of a function algebraically?
A
Plug in -x for x. See if the result is f(x), -f(x), or neither
8
Q
What is the only function that is both even and odd?
A
f(x) = 0
