And here is an inequality showing a group of numbers equal to or greater than 5 and less than 7: The span of numbers included in the group is often imagined as being on a number line, usually the x-axis.

However, it is really not a letter of the alphabet. An interval such aswhere both endpoints are excluded is called an open interval. Here is this group of numbers expressed with interval notation: This same set could be described in another type of notation called interval notation.

Here are some more examples: Now consider the group of numbers that are equal to 5 or greater than 5.

This interval notation would be interpreted just like the interval above, except: That is, 5 is excluded from the group, but the numbers directly to the right of 5 are included.

Q denotes the set of rational numbers fractions. The statement using the inequalities above joined by the word or means that x is a number in the set we just described, and that you will find that number somewhere less than 5 or somewhere greater than 5 on the number line.

The infinity symbols " " are used to indicate that the set is unbounded in the positive or negative direction of the real number line. However, this notation can be used to describe any group of numbers.

Our example becomes the interval -2,5]. How could we write down in interval notation?

First, stated as inequalities this group looks like this: That is, the set of numbers goes all the way to positive infinity. Let us go through one last simple example. The second would start just to the right of 7, but not including 7, and continue to the right down the number line up to and including So intervals are not like doors, they can be open and closed at the same time.

Special symbols are used to denote important sets: So, we see that interval notation is useful for stating the members of groups of numbers. If the set consists of several disconnected pieces, we use the symbol for union " ": Beyond that, set notation uses descriptions: The first would start at negative infinity and proceed toward the right down the number line up to and including 5.Jul 06, · Once you've found these values, write the domain as the variable equal to all real numbers except for the excluded numbers.

If the function has a square root in it, set the terms inside the radicand to be greater than or equal to %(36). So -1 cannot be in the domain, because we cannot divide by 0. Thus, the answer is C: all real numbers except for The general procedure to finding domain of.

is all real numbers except zero (since at x = 0, the function is undefined: division by zero is not allowed!). The range is also all real numbers except zero. You can see that there is some point on the curve for every y -value except y = 0.

A Set is a collection of things (usually numbers). Example: {5, 7, 11} is a set. But we can also "build" a set by describing what is in it. Here is a simple example of set-builder notation: It says "the set of all x's, such that x is greater than 0. What is the "standard" way to denote all positive (or non-negative) real numbers?

I'd think $$ \mathbb R^+ $$ but I believe that that is usually used to denote "all real numbers including infinit. Domain and Range of Rational Functions The domain of a function f x is the set of all values for which the function is defined, and the range So, the range of the function is.

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