How to Tell If a Function is Even or Odd PDF

1/9/25, 10:44 PM Determining if a Function is Even or Odd Student: How to Tell if a Function is Even or Odd https://study.com/skill/learn...

1/9/25, 10:44 PM Determining if a Function is Even or Odd Student: How to Tell if a Function is Even or Odd https://study.com/skill/learn/how-to-tell-if-a-function-is-even-or-odd-explanation.html 1. Determine if the function f (x) = x 2 + 5 is Even, Odd, or Neither.  Even, since f (x) = f (−x) Even, since f (x) = −f (−x) Odd, since f (x) = −f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) 2. Determine if the function f (x) = x + 15 is Even, Odd, or Neither. Odd, since f (x) = −f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = f (−x) Even, since f (x) = f (−x) 3. Determine if the function f (x) = x 7 is Even, Odd, or Neither. Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x)  Odd, since f (x) = −f (−x) Even, since f (x) = f (−x) Odd, since f (x) = f (−x) 4. Determine if the function f (x) = x 3 − 15 is Even, Odd, or Neither. Odd, since f (x) = −f (−x) Even, since f (x) = −f (−x) Even, since f (x) = f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) 5. Determine if the function f (x) = x 4 + x 3 + 10 is Even, Odd, or Neither. Odd, since f (x) = −f (−x) Even, since f (x) = −f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Even, since f (x) = f (−x) https://study.com/skill/print/practice/determining-if-a-function-is-even-or-odd-questions.html 1/6 1/9/25, 10:44 PM Determining if a Function is Even or Odd 6. Determine if the function f (x) = x 2 is Even, Odd, or Neither.  Even, since f (x) = f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Even, since f (x) = −f (−x) Odd, since f (x) = −f (−x) 7. Determine if the function f (x) = −x 2 is Even, Odd, or Neither. Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x)  Even, since f (x) = f (−x) Odd, since f (x) = −f (−x) Even, since f (x) = −f (−x) 8. Determine if the function f (x) = x 3 is Even, Odd, or Neither. Even, since f (x) = f (−x)  Odd, since f (x) = −f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = f (−x) 9. Determine if the function f (x) = −x 3 is Even, Odd, or Neither. Odd, since f (x) = f (−x) Even, since f (x) = f (−x)  Odd, since f (x) = −f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) 10. Determine if the function f (x) = x 4 + x 2 + x − 5 is Even, Odd, or Neither. Even, since f (x) = −f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = −f (−x) Even, since f (x) = f (−x) 11. Determine if the function f (x) = x 10 is Even, Odd, or Neither.  Even, since f (x) = f (−x) Even, since f (x) = −f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = −f (−x) https://study.com/skill/print/practice/determining-if-a-function-is-even-or-odd-questions.html 2/6 1/9/25, 10:44 PM Determining if a Function is Even or Odd 12. Determine if the function f (x) = 16 − x − x 3 is Even, Odd, or Neither. Even, since f (x) = f (−x) Even, since f (x) = −f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = −f (−x) 13. Determine if the function f (x) = −x 2 − x 4 is Even, Odd, or Neither. Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Even, since f (x) = −f (−x) Odd, since f (x) = −f (−x)  Even, since f (x) = f (−x) 14. Determine if the function f (x) = x 5 is Even, Odd, or Neither. Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = f (−x)  Odd, since f (x) = −f (−x) Even, since f (x) = f (−x) 15. Determine if the function f (x) = −x 5 is Even, Odd, or Neither. Even, since f (x) = f (−x)  Odd, since f (x) = −f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = f (−x) 16. Determine if the function f (x) = 9 + x + x 2 is Even, Odd, or Neither. Even, since f (x) = f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = −f (−x) Odd, since f (x) = f (−x) 17. Determine if the function f (x) = x 2 + x 6 + x 10 is Even, Odd, or Neither. Odd, since f (x) = f (−x)  Even, since f (x) = f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = −f (−x) https://study.com/skill/print/practice/determining-if-a-function-is-even-or-odd-questions.html 3/6 1/9/25, 10:44 PM Determining if a Function is Even or Odd 18. Determine if the function f (x) = −x 2 − x 6 − x 10 is Even, Odd, or Neither. Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = −f (−x) Odd, since f (x) = f (−x)  Even, since f (x) = f (−x) 19. Determine if the function f (x) = x + x 3 + x 5 is Even, Odd, or Neither. Odd, since f (x) = f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Even, since f (x) = f (−x)  Odd, since f (x) = −f (−x) 20. Determine if the function f (x) = −x − x 3 − x 5 is Even, Odd, or Neither. Odd, since f (x) = f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Even, since f (x) = f (−x)  Odd, since f (x) = −f (−x) 21. Determine if the function f (x) = sin x + 2 is Even, Odd, or Neither. Even, since f (x) = f (−x) Odd, since f (x) = −f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = f (−x) 22. Determine if the function f (x) = sin(x ) 2 is Even, Odd, or Neither. Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = −f (−x) Even, since f (x) = −f (−x)  Even, since f (x) = f (−x) 23. Determine if the function f (x) = sin(x ) 3 is Even, Odd, or Neither. Odd, since f (x) = f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x)  Odd, since f (x) = −f (−x) Even, since f (x) = f (−x) https://study.com/skill/print/practice/determining-if-a-function-is-even-or-odd-questions.html 4/6 1/9/25, 10:44 PM Determining if a Function is Even or Odd 24. Determine if the function f (x) = sin(−x) is Even, Odd, or Neither. Odd, since f (x) = f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x)  Odd, since f (x) = −f (−x) Even, since f (x) = f (−x) 25. Determine if the function f (x) = sin(−x ) 2 is Even, Odd, or Neither.  Even, since f (x) = f (−x) Even, since f (x) = −f (−x) Odd, since f (x) = −f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) 26. Determine if the function f (x) = sin(−x ) 3 is Even, Odd, or Neither.  Odd, since f (x) = −f (−x) Odd, since f (x) = f (−x) Even, since f (x) = f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) 27. Determine if the function f (x) = cos(x) + sin(x) − 3 is Even, Odd, or Neither. Even, since f (x) = f (−x) Odd, since f (x) = f (−x) Odd, since f (x) = −f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) 28. Determine if the function f (x) = cos(−x) + x is Even, Odd, or Neither. Odd, since f (x) = −f (−x) Even, since f (x) = f (−x)  Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = f (−x) 29. Determine if the function f (x) = cos(x ) 2 is Even, Odd, or Neither. Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Even, since f (x) = −f (−x)  Even, since f (x) = f (−x) Odd, since f (x) = −f (−x) https://study.com/skill/print/practice/determining-if-a-function-is-even-or-odd-questions.html 5/6 1/9/25, 10:44 PM Determining if a Function is Even or Odd 30. Determine if the function f (x) = cos(−x ) 2 is Even, Odd, or Neither.  Even, since f (x) = f (−x) Odd, since f (x) = −f (−x) Neither, since f (x) ≠ f (−x) and f (−x) ≠ −f (x) Odd, since f (x) = f (−x) https://study.com/skill/print/practice/determining-if-a-function-is-even-or-odd-questions.html 6/6