How do I graph a horizontal asymptote of (x+3)/2?

Question

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

Answer 1

(x+3)/2 is indeed a slant (horizontal) asymptote of (x²+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.