Mathematical Methods · Unit 1 · Functions and relations · Reciprocal functions
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Consider the function \( f(x) = \frac{2x - 3}{x + 1} \) with domain \( \mathbb{R} \setminus \{-1\} \). (a) Determine the equations of both asymptotes of the graph of \( y = f(x) \). (2 marks) (b) Find the coordinates of both intercepts of the graph. (1 mark) (c) Determine the coordinates of one additional point on the graph where \( x = 1 \). (1 mark)
The graph shows a reciprocal function of the form f(x) = (ax + b)/(x + c), where a, b, and c are constants. The graph has a vertical asymptote at x = -2, a horizontal asymptote at y = 3, and passes through the point (1, 2). Determine the values of a, b, and c.
The function $f(x) = \frac{3}{x - 2} + 1$ is defined for all real $x$ except $x = 2$. Which of the following correctly describes the asymptotes of the graph of $f$?