Question

Question #bc921

Answer 1

Rational function, asymptotes x=-3, x=-3, y=1, symmetrical about y-axis.

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.