Alg_Complete

# If x 0 x f x x if x 0 this is a piecewise function

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Unformatted text preview: Slope of Asymptotes Equations of Asymptotes and ( h - a, k ) y=k± b a ± b ( x - h) a y=k± b a b ( x - h) a Note that the difference between the two forms is which term has the minus sign. If the y term has the minus sign then the hyperbola will open left and right. If the x term has the minus sign then the hyperbola will open up and down. We got the equations of the asymptotes by using the point-slope form of the line and the fact that we know that the asymptotes will go through the center of the hyperbola. Let’s take a look at a couple of these. Example 1 Sketch the graph of each of the following hyperbolas. 2 2 ( x - 3) - ( y + 1) = 1 [Solution] (a) 25 49 2 y 2 (b) - ( x + 2 ) = 1 [Solution] 9 Solution (a) Now, notice that the y term has the minus sign and so we know that we’re in the first column of the table above and that the hyperbola will be opening left and right. The first thing that we should get is the center since pretty much everything else is built around that. The center in this case is ( 3, -1) and as always watch the signs! Once we have the center we can get th...
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