Function Domain WorksheetLesson 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:
- 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 , then 2x + 4 ≥ 0, or x ≥ -2.
- 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.
- 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
Function Domain WorksheetFind all possible values for the domain of the function shown.
- f(x) = 3x2 - 4
- H(x) = x - 1
- g(x) =
- z(x) =
- w(x) = +x+x - 1x + 1
- Z(x) =
- h(x) =
- c(x) = x2 - 8x + 12
- v(t) = 1000 - (-32.2)t22
- 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) =
- j(x) =
- f(x) = (2x + 3)
- K(x) =
- P(x) =
Function Domain Worksheet: Answer KeyThis content is for teachers only, and can only be accessed with a site subscription.
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