Functions: Even, Odd, or Neither
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 |2. f(x)= [pic]x2 |3. f(x)= (x+2)2 |
| |[pic] | |
|[pic] |Is this function even? |[pic] |
|Is this function even? | |Is this function even? |
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|4. f(x)= x2 + 2 |5. f(x)= (x – 2)2 |6. f(x)= x2 – 2 |
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|[pic] |[pic] |[pic] |
|Is this function even? |Is this function even? |Is this function even? |
| | | |
| | | |
| | | |
| | | |
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|7. f(x)= [pic] |8. f(x)= [pic] | |
|[pic] |[pic] | |
|Is this function even? |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 |10) f(x)= x3 |
|[pic] |[pic] |
|Is this function odd? |Is this function odd? |
| | |
| | |
|11) f(x)= (x – 2)3 |12) f(x)= x3 -2 |
|[pic] |[pic] |
|Is this function odd? |Is this function odd? |
|13) f(x)= 2x3 |14) f(x)= [pic] |
|[pic] |[pic] |
|Is this function odd? |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)= [pic] ____________________________
f(x)= x2 ____________________________ f(x)= [pic] ___________________________
f(x)= x3 ____________________________ f(x)= [pic] ____________________________
DESIDE IF THE FOLLOWING FUNCTIONS ARE ODD, EVEN OR NEITHER:
1) f(x)= [pic]x2 2) f(x)= (x+2)2 3) f(x)= x2 + 2 4) f(x)= [pic]
5) f(x)= x 6) f(x)= x3 – 3 7) f(x)= 2x3 8) f(x)= [pic]
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