Math Problem Statement

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

Solution

The graph of the function g(x)=(x9)3g(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)g(x)?
  4. What are the key features (such as intercepts) of the graph g(x)=(x9)3g(x) = -(x - 9)^3?
  5. How would the graph change if the function were g(x)=(x9)3g(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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Functions
Transformations of Functions

Formulas

g(x) = -(x - 9)^3
Transformation of cubic functions

Theorems

Transformation Theorem
Reflection over the x-axis
Horizontal Shift

Suitable Grade Level

Grades 9-12