- Without calculus, sketch the graph of \(g(x)\), where \(g(x)=-2-\dfrac{3}{x}\)
- In your answer label all asymptotes and any intercepts. (3 marks)
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- Express the range of \(g(x)\) in set notation. (1 mark)
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Show Answers Only
a.
b. \(\text{Range} \ \ y \in(-\infty,-2) \cup(-2, \infty)\)
Show Worked Solution
a. \(\text{As} \ \ x \rightarrow \infty, g(x) \rightarrow-2^{-}; \text{As} \ \ x \rightarrow-\infty, g(x) \rightarrow-2^{+}\)
\(\text{As} \ \ x \rightarrow 0^{+}, g(x) \rightarrow-\infty; \text{As} \ \ x \rightarrow 0^{-}, g(x) \rightarrow \infty\)
\(\text{Intercept} \ (x \text {-axis}):-2-\dfrac{3}{x}=0 \ \Rightarrow \ 2 x=-3 \ \Rightarrow \ x=-\dfrac{3}{2}\)
b. \(\text{Range} \ \ y \in(-\infty,-2) \cup(-2, \infty)\)
