6B - Cubed root function

Learning intentions:

In this section we will examine:

    • The cubed root function and its transformations (dilations, reflections and translations).
    • How to graph the cubed root function from a given equation.

The cubed root graph

The cubed root function has a general form:

    • All cubed root graphs have the same shape, they are just transformed (dilated, reflected and translated) according to the values of the parameters a, n, h and k.

Introduction to the cubed root graph

Consider the following numbers and their cubed roots:

Table 1 - The cube root of perfect cubes.

If we plot these point on a set of axes we can see the shape of the cubed root graph:

Figure 1 - The cubed root graph (click image to enlarge).

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Success criteria:

You will be successful if you can:

    1. Identify and describe transformations of the cubed root graph.
    2. Sketch the cubed root graph from a given equation.
    3. Label endpoints and axial intercepts with their coordinates.