https://file.aiquickdraw.com/mathbot/file/1728273347568zabt4r1t.jpg

The question in your image asks for the amplitude of the function \( y = -3 \sin(x) \), and also asks to identify the correct graph of this function from the given options.

### 1. **Amplitude of the function:**
   The general form of the sine function is \( y = A \sin(x) \), where \( A \) represents the amplitude. The amplitude is the distance from the midline of the wave to the peak (or trough), which is always a positive number.

   In the given function \( y = -3 \sin(x) \), the coefficient \( -3 \) indicates that the amplitude is \( |A| = 3 \). The negative sign indicates a reflection over the x-axis, but it does not affect the amplitude.

   **Answer: The amplitude is 3.**

### 2. **Correct graph of the function:**
   The function \( y = -3 \sin(x) \) is a sine function with:
   - Amplitude of 3.
   - A reflection over the x-axis (because of the negative sign).
   - The period of a standard sine function, \( 2\pi \), remains unchanged since the coefficient of \( x \) is 1.

   Now, you can identify the correct graph:
   - The graph should have peaks and troughs reaching 3 and -3, respectively.
   - It should be reflected over the x-axis, meaning the first half of the sine wave should start by going downward.

   Based on this, option **B** looks like the correct graph since it shows a sine wave with a reflection and an amplitude of 3.

Would you like more details on any part of this explanation? Here are some follow-up questions you can explore:

1. What effect does the negative sign in front of the sine function have on the graph?
2. How would the graph change if the coefficient of \( x \) were something other than 1 (e.g., \( y = 3 \sin(2x) \))?
3. What is the period of the function \( y = \sin(x) \), and how does it relate to the graph?
4. How would you graph \( y = 3 \cos(x) \) and how does it compare with \( y = 3 \sin(x) \)?
5. What is the formula for determining the amplitude and period of a general trigonometric function?

**Tip**: When graphing sine or cosine functions, always start by identifying the amplitude, period, and any reflections or phase shifts to guide your plot.

Graph the following function over the interval [-2π, 2π]. Give the amplitude. y = -3sin(x). Which of the following is the correct graph of the function y = -3sin(x)? What is the amplitude of the function y = -3sin(x)?

Learn how to graph the function y = -3sin(x) over the interval [-2π, 2π] and find its amplitude. This problem involves understanding trigonometric graphing concepts, amplitude calculations, and reflections over the x-axis. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation