Honors Even and Odd Functions wkst

Even and Odd Functions
If the graph of a function f is symmetric with respect to the y-axis, we say that it is an even
f − x = f x .
function. That is, for each x in the domain of f, ( ) ( )
If the graph of a function f is symmetric with respect to the origin, we say that it is an odd
f − x =− f x .
function. That is, for each x in the domain of f, ( ) ( )
1. Indicate which of the following functions are even, which are odd, and which are neither.
2. Algebraically, determine whether each function is odd, even, or neither.
4 2
a) f ( x) 3x 5x
17
f x = x
= − + b) ( )
7 3
3
c) f ( x) = 12x + 6x − 2x
d) f ( x) x
= 4 − 7
f x = x + 2x+
2
e) ( )
2
f) f ( x)
2
x − 5
=
3
2x
+ x
3. The graphs of an odd function are symmetric about the origin. What geometric property
characterizes even functions
4. Suppose f is an odd function whose domain includes zero. Explain why f(0) = 0 must be
true.
5. Can a function be both even and odd (Hint: Consider constant functions of the form
f(x) = c.

6. Each of the graphs below shows a portion of a graph of an even function over the interval
[-5, 5]. Complete these graphs.
7. Which graph(s) below could be a portion of a graph of an odd function over the interval
[-5, 5] Complete these graphs.
8. Table A shows a portion of a table of an even function and table B shows a portion of a
table of an odd function. Complete these tables.
Table A
Table B
-5 8 -5 -6
-4 6 -4
-3 -3 -2
-2 -2
-1 -2 -1
0 0
1 1 3
2 0 2 5
3 4 3
4 4 -3
5 5