SOLUTION: hey there, Any help would be appreciated, question is as follows : Sketch a graph of the following function. label all discontinuities, axes, intercepts and asymptotes for

Algebra ->  Graphs -> SOLUTION: hey there, Any help would be appreciated, question is as follows : Sketch a graph of the following function. label all discontinuities, axes, intercepts and asymptotes for      Log On


   

Question 937993: hey there,
Any help would be appreciated,
question is as follows :
Sketch a graph of the following function. label all discontinuities, axes, intercepts and asymptotes for
f(X) x^2 +2x -3/x^2 + x - 6
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Like THIS:
f(x)=(x^2+2x-3)/(x^2+x-6)

Rendered into this:
f%28x%29=%28x%5E2%2B2x-3%29%2F%28x%5E2%2Bx-6%29

Factor the parts.

%28%28x-1%29%28x%2B3%29%29%2F%28%28x-2%29%28x%2B3%29%29

One root, one vertical asymptote, one undefined point.

Root at x=1;
Vertical asymptote at x=2;
Discontinuous for x=-3.
Vertical Axis intercept x=1%2F2.

graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%5E2%2B2x-3%29%2F%28x%5E2%2Bx-6%29%29

Look again at the original function. The degree of numerator and denominator are equal. As x goes unbounded either to positive or to negative infinity, the two squared terms become increasingly more important to the value of f. The value of the function approaches but never reaches 1. MEANING: The horizontal asymptote is y=1.