So let's say that I have the function f(x) defined as, so once again, Little bit more concrete, with an example. The set of all possible, all possible outputs. Of all of the things that the function could output, that is going to make up the range. It from this function, that thing is going to be in the range, and if we take the set Something, and by definition, because we have outputted Something from the domain, it's going to output Of definitions for range, but the most typical definition for range is "the set of all possible outputs." So you give me, you input ![]() The range, and the most typical, there's actually a couple That is called the range of the function. Outputs that the function could actually produce? And we have a name for that. The focus of this video is, okay, we know the set ofĪll of the valid inputs, that's called the domain,īut what about all, the set of all of the Thing to think about, and that's actually what Is outside of the domain and try to input it into this function, the function will say, "hey, wait wait," "I'm not defined for that thing" "that's outside of the domain." Now another interesting Outside of the domain, let me do that in a different color. If this is the domain here, and I take a value here,Īnd I put that in for x, then the function is A domain is the set of all of the inputs over which the function is defined. To product an output that we would call "f(x)." And we've already talked a little bit about the notion of a domain. It is going to map that, or produce, given this x, it's going "f", but "f" is the letter most typically used for functions, that if I give it an input, a valid input, if I give it a valid input,Īnd I use the variable "x" for that valid input, it is The square root of negative values is non-real.A review, we know that if we have some function,.Most basic formulas can be evaluated at an input. Using descriptive variables is an important tool to remembering the context of the problem. Remember that, as in the previous example, x and y are not always the input and output variables. For the range, we have to approximate the smallest and largest outputs since they don’t fall exactly on the grid lines. In interval notation, the domain would be and the range would be about. The graph would likely continue to the left and right beyond what is shown, but based on the portion of the graph that is shown to us, we can determine the domain is 1975 ≤ y ≤ 2008, and the range is approximately 180 ≤ b ≤ 2010. The output is “thousands of barrels of oil per day”, which we might notate with the variable b, for barrels. In the graph above, the input quantity along the horizontal axis appears to be “year”, which we could notate with the variable y. Likewise, since range is the set of possible output values, the range of a graph we can see from the possible values along the vertical axis of the graph.īe careful – if the graph continues beyond the window on which we can see the graph, the domain and range might be larger than the values we can see. Remember that input values are almost always shown along the horizontal axis of the graph. Since domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the graph. We can also talk about domain and range based on graphs. ![]() Remember when writing or reading interval notation: using a square bracket [ means the start value is included in the set using a parenthesis ( means the start value is not included in the set. These numbers represent a set of specific values. However, occasionally we are interested in a specific list of numbers like the range for the price to send letters, p = $0.44, $0.61, $0.78, or $0.95. Using inequalities, such as 0 <</a> c ≤ 163, 0 < w ≤ 3.5, and 0 < h ≤ 379 imply that we are interested in all values between the low and high values, including the high values in these examples.
This is one way to describe intervals of input and output values, but is not the only way. In the previous examples, we used inequalities to describe the domain and range of the functions. Since possible prices are from a limited set of values, we can only define the range of this function by listing the possible values. Technically 0 could be included in the domain, but logically it would mean we are mailing nothing, so it doesn’t hurt to leave it out. Since acceptable weights are 3.5 ounces or less, and negative weights don’t make sense, the domain would be 0 < w ≤ 3.5. Suppose
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