In this part you do not have to sketch the graph and you may even be given the sketch of the graph to start with. For a quadratic equation of the form \(y = k{(x - a)^2} + b\), the following diagram ...

In a function such as sine or cosine, we could also have a translation of the form: \(y = \sin (x - a)^\circ\) where \(a\) is called the phase angle. This is when the graph of the function has been ...

In this paper the generating function for the numbers of variations with repetitions and a certain type of restrictions is determined. The variations in question are connected with paths in ...