A mathematical function is a formula that takes an input, x, applies a set of calculations to it, and produces an output called y. By calculating a function at a large number of set intervals, it is ...

👉 Learn how to graph piecewise functions. A piecewise function is a function which has more than one sub-function for different sub-intervals (sub-domains) of the function's domain. To graph a ...

If you have trouble remembering how to graph different mathematical functions, these simple figures with their dancing arms can help. At the very least, they’ll make you think of math every time you ...

👉 Learn how to graph exponential functions involving vertical shift. An exponential function is a function that increases rapidly as the value of x increases. To graph an exponential function, it is ...

A translation is a shift of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. If \(f(x) = x^2\), then \(f(x) + a = x^2 + a\). The value of \(a\) ...

A function is a way of describing what happens to an input variable, in order to get the output result. \(\text{Input} \rightarrow \text{FUNCTION} \rightarrow \text{Output}\) If we think of a simple ...