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