x^2\) is the same as the graph of \(y = x^2\). Writing equations as functions in the form \(f(x)\) is useful when applying translations and reflections to graphs. If \(f(x) = x^2\), then \(f(x ...

\(y = x^2 + a\) represents a translation parallel to the \(y\)-axis of the graph of \(y = x^2\). If \(a\) is positive, the graph translates upwards. If \(a\) is negative, the graph translates ...

Graphs of Sine and Cosine 1.2 An applet illustrating how the graphs of sine and cosine are related to the unit circle. Transformations of Functions 1.3 An applet illustrating how transformations ...