# Function Domain Worksheet

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## 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:

- Denominators can't be equal to zero. Thus, if a denominator is (x - 1), we have x - 1 ≠ 0, or x ≠ 1
- 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.
- n
^{th}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. - 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.
- 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. - 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

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## Function Domain Worksheet

Find all possible values for the domain of the function shown.- f(x) = 3x
^{2}- 4

- H(x) = 2x + 1x - 1

- g(x) = 2x - 5

- z(x) = 310x - 2

- w(x) = +3x+3x - 13x + 1

- Z(x) = 1 - x1 + x

- h(x) = x
^{2}- 5x + 6

- c(x) = 1x
^{2}- 8x + 12

- v(t) = 1000 - (-32.2)t12
^{2}

- 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?

- k(x) = x - 2x + 3

- j(x) = 5xx - 1

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

- K(x) = x
^{3}+ 4x^{2}- 4x - 16

- P(x) = x
^{2}- 1x^{2}- 4

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## Function Domain Worksheet: Answer Key

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