Question #bc921

1 Answer
Roy E.
Oct 27, 2017

Rational function, asymptotes x=-3, x=-3, y=1, symmetrical about y-axis.enter image source here

Explanation:

The denominator factorises into (x-3)(x+3) so there vertical asymptotes at x=+3 and x=-3. For large values of x both positive and negative the expression is nearly 1. (Alternatively, the expression=(x^2-9+9)/(x^2-9)=1+9/(x^2-9, which is clearly positive whenever |x|>3 and tends to 1 as x tends to ± ∞.) Replacing x with -x leaves the expression unchanged, so the graph is symmetrical about the y-axis.

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