SOLUTION: graph F(x) = x-2 there is a line under x-2 x+4

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Question 65116: graph
F(x) = x-2 there is a line under x-2
x+4
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
graph
F%28x%29=%28x-2%29%2F%28x%2B4%29
Because the leading terms in the denominator and numerator have the same degree and coefficients, there is a horizontal asymptote of y=1/1=1. I usually draw a faint dashed line for the asymptotes, because your graph can't equal that.
There is a vertical asymptote where the rational function is undefined (where the denominator=0).
The vertical asymptote is:
x+4=0
x+4-4=0-4
x=-4 Draw a faint dashed line there (unfortunatley this program is going to draw a solid dashed line there.)
Pick two numbers on both sides of the asymptote to plot.
If x=-8
f%28-8%29=%28-8-2%29%2F%28-8%2B4%29
f%28-8%29=-10%2F%28-4%29
f%28-8%29=5%2F2 or 2.5
Plot (-8,5/2)
If x=-6
f%28-6%29=%28-6-2%29%2F%28-6%2B4%29
f%28-6%29=-8%2F%28-2%29
f%28-6%29=4
Plot (-6,4)
If x=-2
f%28-2%29=%28-2-2%29%2F%28-2%2B4%29
f%28-2%29=-4%2F2
f%28-2%29=-2
Plot (-2,-2)
If x=0
f%280%29=%280-2%29%2F%280%2B4%29
f%280%29=-2%2F4
f%280%29=-1%2F2
Plot (0,-1/2)
This equation has an x-intercept when the numerator=0.
x-2=0
x-2+2=0+2
x=2 Plot (2,0)
After you connect the points remembering not to cross the asymptotes you get this: Note this program draws in the vertical asymptote x=-4, it is not part of the graph.
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-2%29%2F%28x%2B4%29%29
Happy Calculating!!!