X is actually the independent variable and Y is the dependent because the Y value depends on what X is. For example, if the function is Y = 2X, then you would put in the X (let's say 4) and …

Rearranging to solve for the variable you want to measure, you get a function (as long as there's not multiple outputs for any input)! Functions involve anything with an independent and …

If any x-coordinate goes with two or more y-coordinates, then the relation is not a function. Graphically, if any vertical line passes through two or more points, then the graph (or relation) …

Because we are not explicitly defining y as a function of x, and explicitly getting y is equal to f prime of x, they call this-- which is really just an application of the chain rule-- we call it implicit …

So whenever you're asked whether something is a function of something else, you're really just saying, look, for any input x, does it map to exactly one y? So if we say y is a function of x, in …

To add on to Matthew, implicit differentiation is basically used when we have a function of x and y where y is a function of x. But, it is hard or impossible to split up x and y that we end up …

In the following table, is y a function of x? In order for y to be a function of x, for any x that we input into our little function box-- so let's say this is y as a function of x.

Many functions are equations. But, they don't have to be. If you have a set of ordered pairs where each x-value relates to only one y-value, then you have a function. For example: { (2,5); (3,8); …

So in order for y to be a function of x, for any x that you input into the function, any x for which the function is defined. So let's say we have y is equal to f of x.

About this unit A function is like a machine that takes an input and gives an output. Let's explore how we can graph, analyze, and create different types of functions. Unit guides are here! …