A curve has the equation \(y = f(x)\), where \(f(x) = \dfrac{2x+1}{x-3}\) for \(x \ne k\).
State the value of \(k\).[1]
Find the equation of the normal to the curve at the point \(x = 4\).[4]
Explain whether \(f\) is an increasing or decreasing function for \(x > 3\).[2]
Determine whether the gradient of the curve is an increasing or decreasing function for \(x > 3\).[3]
The line \(y = c\) does not intersect the curve. By expressing \(\dfrac{2x+1}{x-3}\) as \(a + \dfrac{b}{x-3}\) where \(a\), \(b\) and \(c\) are constants, explain why \(c = 2\).[2]