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? |

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|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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