Without calculus, sketch the graph of \(y=\dfrac{3 x-2}{x}\), labelling all asymptotes and intercepts. (3 marks)
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\(y=\dfrac{3 x-2}{x} \ \Rightarrow \ y=3-\dfrac{2}{x}\)
\(\text{As} \ \ x \rightarrow \infty, y \rightarrow 3^{-} ; \ \text{As} \ \ x \rightarrow-\infty, y \rightarrow 3^{+}\)
\(\text{As} \ \ x \rightarrow 0^{+}, y \rightarrow-\infty ; \ \text{As} \ \ x \rightarrow 0^{-}, y \rightarrow \infty \)