Graphs of exponential functions and logarithmic functions provide a visual insight into their properties, such as growth, decay, and the inverse relationship between them. Graphs of exponential ...

While graphs for cosine and sine functions are similar, those for tangent functions differ significantly from them, sharing only in that they show periodicity and symmetry. Recall \(\tan(x)= ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

A function is a rule that is applied to one set of values to give another set of values. A function can be illustrated on a graph – points are plotted as coordinates and joined by either a straight ...

If \(f(x) = x^2\), then \(af(x) = a(x^2)\). This tells us that we need to multiply each of the \(y\) coordinates on the graph by \(a\) in order to stretch the original graph. Looking at some ...