3x 6 f x x 1 solution so well start off with the

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Unformatted text preview: the graph of f ( x ) = 1 . First, since this is a rational function we are going to have x to be careful with division by zero issues. So, we can see from this equation that we’ll have to avoid x = 0 since that will give division by zero. Now, let’s just plug in some values of x and see what we get. x f(x) -4 -0.25 -2 -0.5 -1 -1 -0.1 -10 -0.01 -100 0.01 100 0.1 10 1 1 2 0.5 4 0.25 So, as x get large (positively and negatively) the function keeps the sign of x and gets smaller and smaller. Likewise as we approach x = 0 the function again keeps the same sign as x but starts getting quite large. Here is a sketch of this graph. First, notice that the graph is in two pieces. Almost all rational functions will have graphs in multiple pieces like this. Next, notice that this graph does not have any intercepts of any kind. That’s easy enough to check for ourselves. © 2007 Paul Dawkins 238 http://tutorial.math.lamar.edu/terms.aspx College Algebra ( ) Recall that a graph will have a y-intercept at the point 0, f ( 0 ) . However, in this case we have to avoid x = 0 an...
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