You can put this solution on YOUR website! To graph these types of equations, you need:
1) Vertical Asymptote (when is denominator 0)
2) Horizontal Asymptote (what is y when x gets very large)
3) Two points, one on either side of vertical asymptote
Denominator is x-3: x-3 = 0 --> x=3
1) Vertical Asymptote is x = 3
Note: As the denominator of a fraction gets larger its value gets closer to zero
So when x is very large h(x) = 0 + 1 = 1
2) Horizontal Asymptote is y = 1
Pick an x_value less than 3 and greater than 3:
Say 2 and 4
3) Two points: (2,0) and (4,2)
Now you can sketch the graph of h(x):
Draw dotted lines for the asymptotes at x=3 and y=1
Plot the points found above
Draw a line through the points without crossing the dotted lines
You should notice you have to draw 2 lines, the lines should get really close to y=1 on either end at go almost vertical at x=3
