10

Consider the function $f(x)=\dfrac{4x+2}{x-2}$, $x\neq2$.

(a) Sketch the graph of $y=f(x)$. On your sketch, indicate the values of any axis intercepts and label any asymptotes with their equations.

(b) Write down the range of $f$.

Consider the function $g(x)=x^{2}+bx+c$. The graph of $g$ has an axis of symmetry at $x=2$.
The two roots of $g(x)=0$ are $-\frac12$ and $p$, where $p\in\mathbb Q$.

(c) Show that $p=\dfrac{9}{2}$.

(d) Find the value of $b$ and the value of $c$.

(e) Find the $y$-coordinate of the vertex of the graph of $y=g(x)$.

(f) Find the product of the solutions of the equation $f(x)=g(x)$.