Graphing Cubic Functions
A step by step tutorial on how to determine the properties of the graph of cubic functions and graph them. Properties, of these functions, such as domain, range, x and y intercepts, zeros and factorization are used to graph this type of functions. Free graph paper is available.
Properties of Cubic FunctionsCubic functions have the formWhere a, b, c and d are real numbers and a is not equal to 0. The domain of this function is the set of all real numbers. The range of f is the set of all real numbers. The y intercept of the graph of f is given by y = f(0) = d. The x intercepts are found by solving the equation The left hand side behaviour of the graph of the cubic function is as follows: If the leading coefficient a is positive, as x increases f(x) increases and the graph of f is up and as x decreases indefinitely f(x) decreases and the graph of f is down. If the leading coefficient is negative, as x increases f(x) decreases the graph of f is down and as x decreases indefinitely f(x) increases the graph of f is up. Example 1f is a cubic function given by
Solution to Example 1
Example 2f is a cubic function given by
Solution to Example 2
Example 3f is a cubic function given by
Solution to Example 3
Example 4f is a cubic function given by
Solution to Example 4
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