Domain & Range

Below is a graph of the cubic function, f(x) = -x³ + 2x² + 3x -1.

Since the function is not modeling a situation, the domain is all real numbers. From the graph, it appears that the range is also all real numbers. On a graph, the range corresponds to the vertical axis. Look up and down to see if there are any end points to help find the range. On the left side of the graph, it keeps going up with no endpoint so the range goes to positive infinity, which can be written as . On the right, the graph keeps going down. The range then goes to negative infinity, . All cubic functions have similar range values.

In the previous chapter, end behavior of polynomials was discussed. Since all odd functions have a cubic-like shaped graph and cubic functions have similar end behavior, odd function graphs will eventually cover all possible values of y and have a range of all real numbers.