5x2 x 4 5 x3 x 2 0 x 6 5 x 3 20 x 2 19 x 2

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Unformatted text preview: 3 , -3 < x < 3 , x > 3 . Also, the largest exponent in the denominator is 2 and since there are no x’s in the numerator the © 2007 Paul Dawkins 241 http://tutorial.math.lamar.edu/terms.aspx College Algebra largest exponent is 0, so by the fact the x-axis will be the horizontal asymptote. Finally, we need some points. We’ll use the following points here. f ( -4 ) = f ( -2 ) = f ( 2) = f ( 4) = 9ö æ ç -4, ÷ 7ø è 9ö æ ç -2, - ÷ 5ø è 9 7 9 5 9ö æ ç 2, - ÷ 5ø è æ 9ö ç 4, ÷ è 7ø 9 5 9 7 Notice that along with the y-intercept we actually have three points in the middle region. This is because there are a couple of possible behaviors in this region and we’ll need to determine the actual behavior. We’ll see the other main behaviors in the next examples and so this will make more sense at that point. Here is the sketch of the graph. Example 3 Sketch the graph of the following function. x2 - 4 f ( x) = 2 x - 4x Solution This time notice that if we were to plug in x = 0 into the denominator we would get division by zero. This means there will not be a y-intercept for this graph. We hav...
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