Math Problem Statement
Below is a portion of the graph of a transformation π(π₯) of π₯3 . Following the Black, Purple, Blue, Red color scheme that is used in the textbook (as illustrated in Example 6 in Section 2.6), give the Black, Purple, Blue, Red sequence of functions that ends with the function that is graphed below. Enter your answer as a sequence of four functions separated by commas. The first term in your sequence should be π₯3 . The last term in your sequence should be the formula that would complete this sentence: The formula for this transfomation is π(π₯)=
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Cubic Functions
Graph Transformations
Formulas
Base cubic function: f(x) = x^3
Reflection: f(x) = -x^3
Vertical shift: f(x) = -x^3 - 6
Horizontal shift: f(x) = -(x - 5)^3 - 6
Theorems
Transformation of functions
Reflections
Shifts
Suitable Grade Level
Grades 9-12
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