Student Question

Analyze the function `x^2+10x+6/x+9`

Expert Answers

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Given `f(x)=x^2+10x+6/x+9` :

(1) The domain is all real numbers except 0: `(-oo,0)uu(0,oo)` . (Possible restrictions on the domain are taking even roots of negative numbers in the reals, taking logarithms of negative numbers in the reals, and as in this case dividing by zero)

(2)There are no horizontal asymptotes. There is a vertical asymptote at x=0.

(3) The end behavior of this graph is `f(x)=x^2+10x+9` , since for large |x| the `6/x` term contributes little.

(4) The graph:

The graph with the graph of y=x^2+10x+9 for comparison:

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