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Unformatted text preview: into regions. In each region graph at
least one point in each region. This point will tell us whether the graph will be above or
below the horizontal asymptote and if we need to we should get several points to
determine the general shape of the graph.
5. Sketch the graph.
Note that the sketch that we’ll get from the process is going to be a fairly rough sketch but that is
okay. That’s all that we’re really after is a basic idea of what the graph will look at.
Let’s take a look at a couple of examples. Example 1 Sketch the graph of the following function.
3x + 6
f ( x) =
So, we’ll start off with the intercepts. The y-intercept is, f ( 0) = 6
-1 Þ ( 0, -6 ) The x-intercepts will be, 3x + 6 = 0
x = -2 Þ ( -2, 0 ) Now, we need to determine the asymptotes. Let’s first find the vertical asymptotes. x -1 = 0 Þ x =1 So, we’ve got one vertical asymptote. This means that there are now two regions of x’s. They
© 2007 Paul Dawkins 240 http://tutorial.math.lamar.edu/terms.aspx College Algebra are x < 1 and x > 1 .
Now, the largest e...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12