Mathematics: GRAPHS Topical Past Paper Questions

The following diagram shows part of the graph of $ f(x) = \frac{k}{x} $, for x > 0, k > 0. Let $ \mathrm{P}\left(p, \frac{k}{p}\right) $ be any point on the graph of $ f $. Line $ L_{1} $ is the tangent to the graph of $ f $ at P. (a) (i) Find $f'(p)$ in terms of $k$ and $p$. (ii…

[Maximum mark: 6] The following diagram shows the graph of $ y = f(x), -3 \leq x \leq 5 $. (a) Find the value of $(f\circ f)(1)$. (b) Given that $ f^{-1}(a)=3 $, determine the value of a. (c) Given that $ g(x) = 2f(x-1) $, find the domain and range of g.

Let $ f(x)=\frac{6x-1}{2x+3} $, for $ x\neq-\frac{3}{2} $. (a) For the graph of $f$, (i) find the y-intercept; (ii) find the equation of the vertical asymptote; (iii) find the equation of the horizontal asymptote. (b) Hence or otherwise, write down $ \lim_{x\to\infty}\left(\frac{…