The equation of a curve $C$ is given by $y=1+\frac{6}{x-3}-\frac{24}{x+3}$. Write down the equat

Question

The equation of a curve $C$ is given by $y=1+\frac{6}{x-3}-\frac{24}{x+3}$. Write down the equations of the asymptotes. Find the coordinates of the points where $C$ meets the axes. Without using a calculator, find the set of values of $y$ for which there are no points on $C$. Sketch $C$.

Accepted Answer

(i) $y=1$, $x=3$, $x=-3$ (ii) $(0, -9)$ and $(9, 0)$ (iii) $-8 < y < 0$

Graphing Techniques - Sketching Rational Functions

Graphing Techniques - Sketching Rational Functions

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