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Understanding Functions: Definitions and Examples

Learn the basics of functions, how to determine if a relation is a function, and solve function problems with clear explanations and examples.

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Understanding Functions: Definitions and Examples

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  1. 1.7 - Functions

  2. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range.

  3. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range.

  4. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range.

  5. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range.

  6. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannot be an x-value repeated!

  7. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated!

  8. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated! Ex.1 Determine if each is a function.

  9. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated! Ex.1 Determine if each is a function. • X Y -6 -4 9 -1 -6 1 1

  10. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated! Ex.1 Determine if each is a function. • X Y -6 -4 9 Y -1 -6 E 1 1 S

  11. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated! Ex.1 Determine if each is a function. • X Y b. -6 -4 9 Y -1 -6 E 1 1 S

  12. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated! Ex.1 Determine if each is a function. • X Y b. -6 -4 9 Y -1 -6 E 1 1 S

  13. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated! Ex.1 Determine if each is a function. • X Y b. -6 -4 9 Y -1 -6 E 1 1 S

  14. 1.7 - Functions • A function is a relation in which each element of the domain is paired with exactly one element of the range. • There cannotbe an x-value repeated! Ex.1 Determine if each is a function. • X Y b. -6 NOT A -4 9 Y FUNC. -1 -6 E 1 1 S

  15. Ex. 2 If f(x) = x2 – 5, find the following:

  16. Ex. 2 If f(x) = x2 – 5, find the following: a. f(-9)

  17. Ex. 2 If f(x) = x2 – 5, find the following: a. f(-9) f(x) = x2 – 5

  18. Ex. 2 If f(x) = x2 – 5, find the following: a. f(-9) f(x) = x2 – 5 f(-9)

  19. Ex. 2 If f(x) = x2 – 5, find the following: a. f(-9) f(x) = x2 – 5 f(-9)

  20. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 Ex. 2 If f(x) = x2 – 5, find the following:

  21. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 Ex. 2 If f(x) = x2 – 5, find the following:

  22. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 Ex. 2 If f(x) = x2 – 5, find the following:

  23. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 Ex. 2 If f(x) = x2 – 5, find the following:

  24. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) Ex. 2 If f(x) = x2 – 5, find the following:

  25. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 Ex. 2 If f(x) = x2 – 5, find the following:

  26. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = Ex. 2 If f(x) = x2 – 5, find the following:

  27. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 Ex. 2 If f(x) = x2 – 5, find the following:

  28. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62 Ex. 2 If f(x) = x2 – 5, find the following:

  29. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 Ex. 2 If f(x) = x2 – 5, find the following:

  30. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 Ex. 2 If f(x) = x2 – 5, find the following:

  31. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 Ex. 2 If f(x) = x2 – 5, find the following:

  32. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 Ex. 2 If f(x) = x2 – 5, find the following:

  33. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 f(4) + 2 = Ex. 2 If f(x) = x2 – 5, find the following:

  34. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 f(4) + 2 = [(4)2 – 5] Ex. 2 If f(x) = x2 – 5, find the following:

  35. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 f(4) + 2 =[(4)2 – 5] Ex. 2 If f(x) = x2 – 5, find the following:

  36. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 f(4) + 2 =[(4)2 – 5] + 2 Ex. 2 If f(x) = x2 – 5, find the following:

  37. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2 = [16 – 5] + 2 Ex. 2 If f(x) = x2 – 5, find the following:

  38. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2 = [16 – 5] + 2 = 11 + 2 Ex. 2 If f(x) = x2 – 5, find the following:

  39. a. f(-9) f(x) = x2 – 5 f(-9) = (-9)2 – 5 = 81 – 5 f(-9) = 76 b. f(6z) f(x) = x2 – 5 f(6z) = (6z)2 – 5 = 62·z2 – 5 f(6z) = 36z2 – 5 c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2 = [16 – 5] + 2 = 11 + 2 f(4) + 2 = 13 Ex. 2 If f(x) = x2 – 5, find the following:

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