G f g x f x 2 x 1 2 3x x 2 2 x

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Unformatted text preview: uld be used with the bottom function. x - x2 + 4 -2 0 -1 3 0 4 1 3 x 2x -1 1 1 2 3 3 5 ( x, y ) ( -2,0 ) ( -1,3) ( 0, 4 ) (1,3) ( x, y ) (1,1) ( 2,3) ( 3,5) Here is a sketch of the graph and notice how we denoted the points at x = 1 . For the top function we used an open dot for the point at x = 1 and for the bottom function we used a closed dot at x = 1 . In this way we make it clear on the graph that only the bottom function really has a point at x = 1 . © 2007 Paul Dawkins 187 http://tutorial.math.lamar.edu/terms.aspx College Algebra Notice that since the two graphs didn’t meet at x = 1 we left a blank space in the graph. Do NOT connect these two points with a line. There really does need to be a break there to signify that the two portions do not meet at x = 1 . Sometimes the two portions will meet at these points and at other times they won’t. We shouldn’t ever expect them to meet or not to meet until we’ve actually sketched the graph. Let’s take a look at another example of a piecewise function. Example 3 Sketch the grap...
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