1. Q UICK P OWER P OINT P RESENTATION ON D OMAINS OF FUNCTIONS

2. Defn: The domain of a function is the set of real numbers (decimal numbers) that when plugged into the function in the place of x will yield a real number (decimal number) after the arithmetic is completed. A real number is not in the domain of the function if when plugged into the function it makes the function “undefined” or “imaginary”.

3. Three basic situations occur when you are looking for the domain of a function. Example 1: This function is very basic. You could plug in any decimal you wish and the arithmetic would give you a decimal. Therefore, the domain would be the set of all decimals (real numbers). In interval notation, all the real numbers off the number line would be: So, that is the domain of the function in Example 1.

4. Sometimes a function will contain a fraction. That can cause a problem with the domain. Example 2: This function has problems when you plug in x = 4 or x = -3 because they make the function undefined. Therefore you can plug in any decimal and do the arithmetic except for 4 and -3. In interval notation that would be: So, that is the domain of Example 2.

5. The last possible problem occurs if the function contains a “square root” symbol. Example 3: This function has problems when x – 5 is negative. Why? Because then you would have the square root of a negative number which is an imaginary number. To find the domain you would then set x – 5 to be positive (which means greater than or equal to zero). So, we would have to solve: which gives us that. In interval notation that is. So, that is the domain of Example 3.