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

2 Answers

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

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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:

brianna09's profile pic

brianna09 | Student, Undergraduate | (Level 3) Honors

Posted on

sorry here is the rest

Given the following rational function:

(a) state the domain.

(b) find the vertical and horizontal asymptotes, if any.

(c) find the oblique asymptotes, if any.

(d)  graph of this function