Eddie S.

asked • 10/14/14# How do I graph a horizontal asymptote of (x+3)/2?

Without using technology, to graph (x^2+x-2)/ (2x-4)

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## 1 Expert Answer

Philip P. answered • 10/14/14

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(x+3)/2 is indeed a slant (horizontal) asymptote of (x

^{2}+x-2)/(2x-4). You should note that (x+3)/2 is the equation of a straight line:y = (1/2)x + 3/2

Where 1/2 is the slope and 3/2 is the y-intercept. To graph a line, all you need is to plot two points on the line then draw a straight line through them. The y-intercept is one point: (0,3/2). To find another point, just pick any value of x and compute the corresponding y. Let's try x = 1:

y = (1/2)*(1) + 3/2

y = 1/2 + 3/2

y = 4/2 = 2

The second point is (1,2). Plot the two points (0,3/2) and (1,2) on the graph and use a straight edge to draw the asymptotic line through them.

Eddie S.

Thanks!

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10/14/14

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