Describe how the given function can be obtained from one of the basic graphs. Then graph the function.

​g(x)equals=minus−​(xminus−99​)cubed

The graph of the function \( g(x) = -(x - 9)^3 \) is shown above. It demonstrates the cubic shape reflected over the x-axis and shifted 9 units to the right.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How does changing the sign of the coefficient affect the graph of a cubic function?
2. What is the effect of a horizontal shift on the graph of a function?
3. How do you find the inflection point of the function \( g(x) \)?
4. What are the key features (such as intercepts) of the graph \( g(x) = -(x - 9)^3 \)?
5. How would the graph change if the function were \( g(x) = (x - 9)^3 \) instead?

**Tip**: Always check for transformations in functions like horizontal shifts, reflections, and vertical stretches/compressions to understand how the graph is altered from its basic form.

Describe how the given function can be obtained from one of the basic graphs. Then graph the function. g(x) = -(x - 9)^3

Learn how to graph the cubic function g(x) = -(x - 9)^3 by applying transformations. This problem involves reflecting the basic cubic graph over the x-axis and shifting it horizontally. Perfect for students in Grades 9-12 studying function transformations.

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