What is the connection between the table graph and function?

Answer 1

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.