A polynomial function without radicals or variables in the denominator. For this type of function, the domain is all real numbers. A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation. A function with a variable inside a radical sign. To find the domain of this type of function, just set the terms inside the radical sign to >0 and solve to find the values that would work for x. A function using the natural log (ln). Just set the terms in the parentheses to >0 and solve. A graph. Check out the graph to see which values work for x. A relation. This will be a list of x and y coordinates. Your domain will simply be a list of x coordinates.

The format for expressing the domain is an open bracket/parenthesis, followed by the 2 endpoints of the domain separated by a comma, followed by a closed bracket/parenthesis. [1] X Research source For example, [-1,5). This means that the domain goes from -1 to 5. Use brackets such as [ and ] to indicate that a number is included in the domain. So in the example, [-1,5), the domain includes -1. Use parentheses such as ( and ) to indicate that a number is not included in the domain. So in the example, [-1,5), 5 is not included in the domain. The domain stops arbitrarily short of 5, i. e. 4. 999… Use “U” (meaning “union”) to connect parts of the domain that are separated by a gap. ’ For example, [-1,5) U (5,10]. This means that the domain goes from -1 to 10, inclusive, but that there is a gap in the domain at 5. This could be the result of, for example, a function with “x - 5” in the denominator. You can use as many “U” symbols as necessary if the domain has multiple gaps in it. Use infinity and negative infinity signs to express that the domain goes on infinitely in either direction. Always use ( ), not [ ], with infinity symbols. Keep in mind that this notation may be different depending on where you live. The rules outlined above apply to the UK and USA. Some regions use arrows instead of infinity signs to express that the domain goes on infinitely in either direction. Usage of brackets varies wildly across regions. For example, Belgium uses reverse square brackets instead of round ones.

So in the example, [-1,5), the domain includes -1.

So in the example, [-1,5), 5 is not included in the domain. The domain stops arbitrarily short of 5, i. e. 4. 999…

For example, [-1,5) U (5,10]. This means that the domain goes from -1 to 10, inclusive, but that there is a gap in the domain at 5. This could be the result of, for example, a function with “x - 5” in the denominator. You can use as many “U” symbols as necessary if the domain has multiple gaps in it.

Always use ( ), not [ ], with infinity symbols.

The rules outlined above apply to the UK and USA. Some regions use arrows instead of infinity signs to express that the domain goes on infinitely in either direction. Usage of brackets varies wildly across regions. For example, Belgium uses reverse square brackets instead of round ones.

f(x) = 2x/(x2 - 4)

f(x) = 2x/(x2 - 4) x2 - 4 = 0 (x - 2 )(x + 2) = 0 x ≠ (2, - 2)

x = all real numbers except 2 and -2

x-7 ≧ 0

x ≧ 7

D = [7,∞)

Now, check the area below -2 (by plugging in -3, for example), to see if the numbers below -2 can be plugged into the denominator to yield a number higher than 0. They do. (-3)2 - 4 = 5 Now, check the area between -2 and 2. Pick 0, for example. 02 - 4 = -4, so you know the numbers between -2 and 2 don’t work. Now try a number above 2, such as +3. 32 - 4 = 5, so the numbers over 2 do work. Write the domain when you’re done. Here is how you would write the domain: D = (-∞, -2) U (2, ∞)

f(x) = ln(x-8)

x - 8 > 0

x - 8 + 8 > 0 + 8 x > 8

D = (8,∞)

A line. If you see a non-vertical line on the graph that extends to infinity in both directions, then all versions of x will be covered eventually, so the domain is equal to all real numbers. A normal parabola. If you see a parabola that is facing upwards or downwards, then yes, the domain will be all real numbers, because all numbers on the x-axis will eventually be covered. A sideways parabola. Now, if you have a parabola with a vertex at (4,0) which extends infinitely to the right, then your domain is D = [4,∞)