what makes an equation a function
vertical line test (every input only has exactly one output)
An equation is called a function if for every input (also called independent variable), there is exactly one output (also called dependent variable). In other words, if we substitute different values for the input, we will get exactly one corresponding output for each input.
It is important to note that not all equations are functions. For example, consider the equation `x^2 + y^2 = 1`. If we substitute different values for x, we can get two different corresponding values for y. Hence, this equation does not represent a function.
To determine if an equation is a function, we can use the vertical line test. If a vertical line intersects a graph in more than one point, then that graph does not represent a function. Conversely, if every vertical line intersects the graph of an equation at most once, then the graph represents a function.
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