Learn how to graph exponential functions involving horizontal shift. An exponential function is a function that increases ...

👉 Learn how to graph quadratic equations in vertex form. A quadratic equation is an equation of the form y = ax^2 + bx + c, ...

Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory, ...

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 ...

Given the graph of a common function, (such as a simple polynomial, quadratic or trig function) you should be able to draw the graph of its related function. The graph of the related function can be ...

JAX offers several composable function transformations (jit, grad, vmap, etc.) that enable writing concise, accelerated code. Here we show how to add your own function transformations to the system, ...