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 f(x)f(x), 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