The vertical is typically the dependent variable (the result of whatever process is causing the event). It could be distance traveled of a projectile, or temperature of a mixed solution, for example.
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X-axis shows increment when is goes up and y-axis show an increment when it goes further to the right side of the graph
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.
Starting from the end the function is an algebraic expression showing the relationship between variables in an equation. The simplest general form being that of two variables with a linear relationship usually shown in the form Y=mx +c where y and x are variables and m and c are constants. The graph, although existing in other forms, is usually shown using Cartesian co-ordinates with a vertical y axis and a horizontal x axis. The above function would appear as a straight line cutting the y axis at value c and with a gradient value m. If m and c had positive values then the line would slope from left to right cutting through the y axis at c and the x axis at -c/m. The table is generally the way of setting out results to show accurate information - usually the results of an experiment or investigation. It is often difficult to visualise or calculate relationships from a table, whereas the graph will illustrate it, and with simple linear relationships the function can be derived by noting the axis intersections. Eg. A straight line cutting through the x axis at -2/3 and the y axis at 2would be expressed as y=3x+2.
what graph uses symbols to represent amounts
You could show the y-axis by distance and the x-axis by time.