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The Purplemath Forums Helping students gain understanding and self-confidence in algebra. Composing with Sets of Points page 1 of 6. Composing functions that are sets of point, Composing functions at pointsComposing functions with other functionsWord problems using compositionInverse functions combining functions graphically worksheet composition.

You could even get fancy and plug in an entire expression for x. In function composition, you're plugging entire functions in for the x. In other words, you're always getting "fancy". But let's start simple. Instead of dealing with functions as formulas, let's deal with functions as sets of xy points: Then f 1 is the y combining functions graphically worksheet of that point.

This is read as " g -compose- f of 1 ", and means "plug 1 into fevaluate, and then plug the result into g combining functions graphically worksheet. The computation can feel a lot easier if I use the following, more intuitive, formatting: Now I'll work in steps, keeping in mind that, while I may be used to doing things from the left to combining functions graphically worksheet right because that's how we readcomposition works from the right to the left or, if you prefer, from the inside out.

Note that they never told us what were the formulas, if any, for f x or g x ; we were only given a list of points. But this list was sufficient for answering the question, as long as we keep track of our x - and y -values. This tells me that I'm going to plug zero into g x combining functions graphically worksheet, simplify, and then plug the result into f x.

In math-speak, g 1 is "not defined"; that is, it is nonsense. Part iii of the above example points out an important consideration regarding domains and ranges. It may be that your composed function the result you get after composing two other functions will have a restricted domain, or at least a domain that is more restricted than you might otherwise have expected. This will be more important when we deal with composing functions symbolically later.

Another exercise of this type gives you two graphs, rather than two sets of points, and has you read the points the function values from these combining functions graphically worksheet. In this case, I will read the points from the graph. So I'll just follow the points on the graphs and compute all the values: You aren't generally given functions as sets of points or as graphs, however. Generally, you have formulas for your functions. So let's see what composition looks like in that case Accessed [Date] [Month] Reviews of Internet Sites: Tutoring from Purplemath Find a local math tutor.

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