SOLUTION: How would I go about figuring out the graph to: {{{ R(x) = 8 - (3/(2x+4)) }}} Thanks!

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Question 959496: How would I go about figuring out the graph to:
+R%28x%29+=+8+-+%283%2F%282x%2B4%29%29++
Thanks!

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Undefined for x=-2, so that will be a horizontal asymptote.

Form into a single rational expression and look to see if any roots.

%288%282x%2B4%29-3%29%2F%282x%2B4%29, excuse for combining steps.

%2816x%2B32-3%29%2F%282x%2B4%29

%2816x%2B29%29%2F%282x%2B4%29

A root at 16x=-29
x=-29%2F16

Notice numerator and denominator are of equal degree. Think about what happens for x unbounded to the left and to the right.....
.... HORIZONTAL asymptote will be y=%2816x%29%2F%282x%29=8.

How to graph:
Root at x=-29/16;
Vertical asymptote x=-2;
Horizontal asymptote y=8.
-
Check signs around the critical x values of -2 and -29/16.

graph%28300%2C300%2C-8%2C2%2C-5%2C15%2C8-%283%2F%282x%2B4%29%29%29