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 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:
- How does changing the sign of the coefficient affect the graph of a cubic function?
- What is the effect of a horizontal shift on the graph of a function?
- How do you find the inflection point of the function ?
- What are the key features (such as intercepts) of the graph ?
- How would the graph change if the function were 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
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