Math Problem Statement
Describe the sequence of transformations that are required to graph based on .
The graph is shifted to the left by 3 units, reflected around the x-axis, compressed vertically, and shifted down 11 units.
The graph is shifted to the right by 3 units, reflected around the x-axis, compressed vertically, and shifted down 11 units.
The graph is shifted to the right by 3 units, reflected around the x-axis, compressed vertically, and shifted up 11 units.
The graph is shifted up 3 units, reflected around the x-axis, compressed vertically, and shifted left 11 units.
Solution
To determine the sequence of transformations, we need to carefully analyze the function's transformations. Let’s break it down step by step.
General Form of Transformations
For a function , transformations typically follow the form
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Math Problem Analysis
Mathematical Concepts
Transformations of Functions
Graph Shifts
Reflections
Vertical Compressions and Stretches
Formulas
y = f(x + h) (horizontal shift)
y = -f(x) (reflection around the x-axis)
y = af(x) (vertical stretch or compression)
y = f(x) + k (vertical shift)
Theorems
Transformation Rules for Functions
Suitable Grade Level
Grades 9-12
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