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Function Domain Worksheet

Lesson Plans > Mathematics > Algebra > Functions
 

Function Domain Worksheet

The following is a worksheet I used with my students as extra practice after discussing things that limit domains, such as square roots and denominators. Important ideas to discuss with students before doing this worksheet:

 

 

  1. Denominators can't be equal to zero. Thus, if a denominator is (x - 1), we have x - 1 ≠ 0, or x ≠ 1
  2. Since it's not possible to take the square root of a negative number, the contents of a radical can't be negative. Thus, if we have
    2x + 4
    , then 2x + 4 ≥ 0, or x ≥ -2.
  3. nth roots have the same restriction only if n is an even number. Thus, cube roots and fifth roots have no restrictions, while fourth roots do.
  4. If the expression inside a radical contains exponents, factor the expression. Then determine in which regions of the real numbers the roduct of those factors is non-negative. For example, if you have (x - 3)(x + 2) >0, we have two points of interest: 3 and -2. If x < -2, both factors are negative, and if x > 3, both factors are positive, resulting in a positive product. Thus, x < -2 or x > 3.
  5. The same concept works for more than two factors. It also works for combinations of multiplication and division. If the number of negative factors is even within a certain region, the product is non-negative.
  6. Since domain restrictions eliminate values in the real numbers, each restriction is cummulative in effect; if one restriction eliminates a number or region, and another restriction eliminates other numbers or regions, the result is the intersection of the allowed regions.
Lesson by Mr. Twitchell

Handouts/Worksheets

Function Domain Worksheet

Find all possible values for the domain of the function shown.

  1. f(x) = 3x2 - 4
     
  2. H(x) =
    2x + 1
    x - 1

     
  3. g(x) =
    2x - 5

     
  4. z(x) =
    3
    10x - 2

     
  5. w(x) =
    3
    x
    +
    3
    x - 1
    +
    3
    x + 1

     
  6. Z(x) =
    1 - x
    1 + x

     
  7. h(x) =
    x2 - 5x + 6

     
  8. c(x) =
    1
    x2 - 8x + 12

     
  9. v(t) =  1000 -
    1
    2
    (-32.2)t2
     
  10. In the previous problem, if the function represents real-time velocity of an object t seconds after launch, how does that change the domain restriction?
     
  11. k(x) =
    x - 2
    x + 3

     
  12. j(x) =
    5
    x
    x - 1

     
  13. f(x) =
    (2x + 3)(x - 3)
    (2x + 3)

     
  14. K(x) =
    x3 + 4x2 - 4x - 16

     
  15. P(x) =
    x2 - 1
    x2 - 4

Function Domain Worksheet: Answer Key

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