Can you graph when a cube root is reflecting show me all possible ways

Here is the graph showing the various reflections of the cube root function. The basic cube root function is included, along with its transformations: reflections over the x-axis, y-axis, and both axes. Each curve is distinct to help visualize the differences.

Would you like further details or any clarifications?

Here are five questions to further explore the concept:

1. What is the effect of horizontal stretching on a cube root function?
2. How does a vertical shift affect the symmetry of the cube root graph?
3. Can a cube root function have asymptotes like some other functions?
4. What happens if you apply both horizontal and vertical stretches simultaneously?
5. How does the domain and range of the cube root function change after reflection?

**Tip:** When transforming functions, always consider how each reflection affects the sign of the inputs and outputs!

Explore the various ways to reflect the cube root function on a graph. This page covers the basic cube root function and its transformations, including reflections over the x-axis, y-axis, and both axes. Suitable for high school students (Grades 9-12).

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