Teacher – Mrs. Volynskaya Pre-Calculus Functions: Even, Odd, or Neither?
NAME _____________________
A function is either even, odd, or neither. You can determine which a function is graphically or algebraically. Graph each function below. If the graph of the function is SYMMETRICAL over Y-axis, it represents an EVEN function. PROVE your answer ALGEBRAICALLY. If a function is even, then f(x)=f(-x). We can prove this by substituting –x into the original function. If f(x) is equal to f(-x), then the function is even.
1. f(x)= x2
Is this function even?
2. f(x)= x2
Is this function even?
3. f(x)= (x+2)2
Is this function even?
4. f(x)= x2 + 2
Is this function even?
5. f(x)= (x – 2)2
Is this function even?
6. f(x)= x2 – 2
Is this function even?
7. f(x)=
Is this function even?
8. f(x)=
Is this function even?
An even function is symmetric over the __________________________.
In each of the following problems, a given function is shown on a graph.
9) f(x)= x
Is this function odd?
10) f(x)= x3
Is this function odd?
11) f(x)= (x – 2)3
Is this function odd?
12) f(x)= x3 -2
Is this function odd?
13) f(x)= 2x3
Is this function odd?
14) f(x)=
Is this function odd?
An odd function is symmetric over the ________________________. If a function is odd, then f(-x)= - f(x). We can prove this by substituting –x into the original function.
A function is either even, odd, or neither. Name which of these each parent function is:
f(x)= x _____________________________ f(x)= ____________________________f(x)= x2 ____________________________ f(x)= ___________________________f(x)= x3 ____________________________ f(x)= ____________________________
DESIDE IF THE FOLLOWING FUNCTIONS ARE ODD, EVEN OR NEITHER:
1) f(x)= x2 2) f(x)= (x+2)2 3) f(x)= x2 + 24) f(x)=
5) f(x)= x 6) f(x)= x3 – 3 7) f(x)= 2x3 8) f(x)=
