Math question, please help?

Question

"Graph the function and identify the vertical asymptote. 
y = 1/(x + 2) + 4" 

Answer 1

The rational function is y = 1/(x + 2) + 4.

It can be written as y  = [1 + 4(x + 2)] / (x + 2) = (4x + 9) / (x + 2).

The graph of rational functions can be recognised by the fact two or more parts.

1). y = (4x + 9) / (x + 2)

To find  y - intercept  x = 0 in the rational function.

y = (4(0) + 9) / (0 + 2)

y  = 9/2.

2). To find x - intercept, let the numarator = 0

4x + 9 = 0

x  = - 9/4.

3)Vertical asymptotes are found  by solving denominator = 0

x + 2 = 0

x = - 2.

Vertical asymptotes is x = - 2.

4).Degree of the numarator = 1 and the degree of denominator = 1.

If the degreeof numerator = degree of denominator, then horizontal asymptote = ratio of leading coefficients.

Therfore, the line y = 4, is the horizontal asymptote.

Now, pick few more x - values, compute the corresponding y  values and flat few more points.

x	y = (4x + 9) / (x + 2)	(x , y )
- 6	y = (4(- 6) + 9) / (- 6 + 2) = (- 24 + 9)/- 4 = - 15/- 4 = 15/4	(- 6, 15/4)
- 5	y = (4(- 5) + 9) / (- 5 + 2) = (- 20 + 9)/- 3 = - 11/- 3 = 11/3	(- 5, 11/3)
- 4	y = (4(- 4) + 9) / (- 4 + 2) = (- 16 + 9)/- 2 = - 7/- 2 = 7/2	(- 4, 7/2)
- 3	y = (4(- 3) + 9) / (- 3 + 2) = (- 12 + 9)/- 1 = - 3/- 1 = 3	(- 3, 3)
- 2	y = (4(- 2) + 9) / (- 2 + 2) = (- 8 + 9)/0 = 1/0 = undefined	undefined
- 1	y = (4(- 1) + 9) / (- 1 + 2) = (- 4 + 9)/1 = 5/1 = 5	(- 1, 5)
0	y = (4(0) + 9) / (0 + 2) = 9/2	(0, 9/2)
1	y = (4(1) + 9) / (1 + 2) = (4 + 9)/3 = 13/3	(1, 13/3)
2	y = (4(2) + 9) / (2 + 2) = (8 + 9)/4 = 17/4	(2, 17/4)

Graph :

1) Draw the coordinate plane.

2) Next dash the horizontal and vertical asympototes

3) Plot the x intercept and coordinate pairs found in the table..

4) Connect the plotted points .

When you draw your graph, use smmoth curves complete the graph.