Math Problem Statement

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Which of the following functions has an amplitude of 3, an axis of equation at y = -2, period 2π, and a phase shift of π to the right?

Solution

Let's analyze the question and the given options step by step to identify the correct function.

Question Details

We are asked to find the function that satisfies:

  1. Amplitude: 33
  2. Axis of equation (vertical shift): y=−2y = -2
  3. Period: 2π2\pi
  4. Phase shift: π\pi to the right

General sinusoidal function:

The general form for sinusoidal functions is:

\quad \text{or} \quad y = A \cos(B(x - \text{Phase Shift})) + D$$ Where: - $$A = \text{Amplitude}$$ - \(B = \frac{2\pi}{\

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Math Problem Analysis

Mathematical Concepts

Amplitude
Phase Shift
Periodicity
Sine and Cosine Functions

Formulas

General sinusoidal function: y = A sin(B(x - Phase Shift)) + D or y = A cos(B(x - Phase Shift)) + D
Period formula: B = 2π / Period

Theorems

-

Suitable Grade Level

Grades 10-12

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