# Combining functions graphs

Questions Tags Users Badges Unanswered. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top. How to find graph of the sum of two functions. What about functions with discontinuities?

Lonidard 2, 1 8 It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help! Paul Regier 6 1. You need to do some analysis. I recommend take the following points. From basic function f and g: See when are f and g zero Find the max and min value of the f and g example: 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 x , y points: Then f 1 is the y -value of that point.

This is read as " g -compose- f of 1 ", and means "plug 1 into f , evaluate, and then plug the result into g ". 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 the right because that's how we read , composition 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 , 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.