Can you show me step by step how to solve the problem and sketch the graph ### Problem Description:3. Sketch the graph of $ f(x) = 2 \sin(x) + 3 $### Explanation:In this problem, we are asked to sketch the graph of the function $ f(x) = 2 \sin(x) + 3 $. Here's how to approach graphing this function:1. **Identify the base function**: The base function here is $ \sin(x) $, which is a standard sine function.2. **Amplitude Adjustment**: The coefficient 2 in front of $ \sin(x) $ affects the amplitude of the sine wave. Instead of oscillating between -1 and 1, the sine wave will now oscillate between -2 and 2.3. **Vertical Shift**: The addition of 3 shifts the entire graph vertically upward by 3 units. Hence, instead of oscillating around the x-axis, the graph will now oscillate around the line $ y = 3 $.4. **Period and Frequency**: Since there is no coefficient affecting the $ x $ inside the sine function, the period and frequency remain unchanged. The standard period of $ \sin(x) $ is $ 2\pi $.### Graph Description:To graph $ f(x) = 2 \sin(x) + 3 $:- Start with the basic shape of $ \sin(x) $, which oscillates between -1 and 1.- Scale the amplitude so that the wave oscillates between -2 and 2.- Shift the entire graph up by 3 units so the centerline of the wave is at $ y = 3 $.- Mark key points such as the maximum (5), minimum (1), and intercept at each half-period (when $ \sin(x) $ is 0, $ f(x) = 3 $).The resulting graph will be a sine wave oscillating between 1 and 5 with a central axis at $ y = 3 $.

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Answered: Can you show me step by step how to…

Math

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Can you show me step by step how to solve the problem and sketch the graph

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Can you show me step by step how to solve the problem and sketch the graph

### Problem Description:
3. Sketch the graph of $ f(x) = 2 \sin(x) + 3 $

### Explanation:
In this problem, we are asked to sketch the graph of the function $ f(x) = 2 \sin(x) + 3 $. Here's how to approach graphing this function:

1. **Identify the base function**: The base function here is $ \sin(x) $, which is a standard sine function.

2. **Amplitude Adjustment**: The coefficient 2 in front of $ \sin(x) $ affects the amplitude of the sine wave. Instead of oscillating between -1 and 1, the sine wave will now oscillate between -2 and 2.

3. **Vertical Shift**: The addition of 3 shifts the entire graph vertically upward by 3 units. Hence, instead of oscillating around the x-axis, the graph will now oscillate around the line $ y = 3 $.

4. **Period and Frequency**: Since there is no coefficient affecting the $ x $ inside the sine function, the period and frequency remain unchanged. The standard period of $ \sin(x) $ is $ 2\pi $.

### Graph Description:
To graph $ f(x) = 2 \sin(x) + 3 $:

- Start with the basic shape of $ \sin(x) $, which oscillates between -1 and 1.
- Scale the amplitude so that the wave oscillates between -2 and 2.
- Shift the entire graph up by 3 units so the centerline of the wave is at $ y = 3 $.
- Mark key points such as the maximum (5), minimum (1), and intercept at each half-period (when $ \sin(x) $ is 0, $ f(x) = 3 $).

The resulting graph will be a sine wave oscillating between 1 and 5 with a central axis at $ y = 3 $.

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