By doing a vertical line test. If you can draw a vertical line and it only passes through the graph once, its a function. If it passes through twice, it is NOT a function.
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if a certain abscissa corresponds to more than one ordinate, then it is not a function.
A zero of a function is a point at which the value of the function is zero. If you graph the function, it is a point at which the graph touches the x-axis.
If the graph of the function is a continuous line then the function is differentiable. Also if the graph suddenly make a deviation at any point then the function is not differentiable at that point . The slope of a tangent at any point of the graph gives the derivative of the function at that point.
Graph that equation. If the graph pass the horizontal line test, it is an inverse equation (because the graph of an inverse function is just a symmetry graph with respect to the line y= x of a graph of a one-to-one function). If it is given f(x) and g(x) as the inverse of f(x), check if g(f(x)) = x and f(g(x)) = x. If you show that g(f(x)) = x and f(g(x)) = x, then g(x) is the inverse of f(x).
This graph fails the vertical line test at x = 3This graph is not the graph of a function.