If your table has two columns--the left one listing various values for x, the "input," and the right one listing corresponding f(x) "output" values, let's say--make sure that there is only one output for every input: meaning there is only one number in each row of the right column.
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The [ 2x + 1 ] represents a function of 'y' .
y0(x) could represent a function of x but usually y(0) represents the function y that is evaluated at x = 0 and so is no longer a function of x but a constant.
If the graph is a function, no line perpendicular to the X-axis can intersect the graph at more than one point.
A derivative of a function represents that equation's slope at any given point on its graph.
take a vertical line, if another line intersects that vertical line at 2 points, then it is a function.In other words,a graph represents a function if each vertical line meets its graph in a unique point.