First find the vertical asymptote by setting the denominator = 0:

2x + 8 = 0
    2x = -8
     x = -4

That is the equation of a vertical line through -4 on the x-axis:

 

Next find the horizontal asymptote by this rule, when the degree
(largest exponent of x in the numerator) is equal to the degree (largest
exponent of x in the denominator)

  

and simplify:





y = 3

 That is the equation of a horizontal line through 3 on the y-axis:



Next get some points on the graph, getting some on the left
of the vertical asymptotes and some on the right:

  x | y
-14 |  3.95
 -9 |  4.9
 -6 |  7.75
 -5 | 12.5
 -3 | -6.5
 -2 | -1.75
  0 |   .625
  1 | 1.1
  6 | 2.05


 
Then sketch in the curve:






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2. How do I graph f(x)=(x+3)/(x^2-25)?

First find the vertical asymptote by setting the denominator = 0:

       x² - 25 = 0
(x - 5)(x + 5) = 0
 
x - 5 = 0;  x + 5 = 0
    x = 5       x = -5

Those is the equation of vertical lines through 5 and -5 on the x-axis:

 

Next find the horizontal asymptote by this rule, when the degree of the
numerator is less than the dgree of the numerator. The horizontal is the
x-axis, the line whose equation is

  

That is the equation of a horizontal line which is the x-axis:



Next get some points on the graph, getting some on the left
and right of each vertical asymptote. In this one you should
get some points real near the asymptotes, at -5.1, -4.9, and 4.9,5.1

  x |  y
-10 |  -.09
 -6 |  -.27
-5.1| -2.08 
-5  | no value (asymptote)
-4.9|  1.91
 -4 | -0.11
 -3 |  0
 -1 | -0.08 
  0 | -0.12
  1 | -0.167
  3 | -0.375
  4 | -0.778
 4.9| -7.98 
  5 | no value (asymptote)
 5.1|  8.02 
  6 | .82
  9 | .21 


 
Then sketch in the curve:



Edwin