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Select the correct answer. The parent cosine function is transformed to create the function m(z) = –2cos(x + 7). Which graphed function has the same amplitude as function m? O A. f(x) 4- 2- lo 37 2- -4- ОВ. f(x) 4- 2- lo 3n -2- -4- OC. f(x) 4- 2- lo -2-

Select the correct answer. The parent cosine function is transformed to create the function m(z) = –2cos(x + 7). Which graphed function has the same amplitude as function m? O A. f(x) 4- 2- lo 37 2- -4- ОВ. f(x) 4- 2- lo 3n -2- -4- OC. f(x) 4- 2- lo -2-

Algebra and Trigonometry (6th Edition)
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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Here is a transcription and detailed explanation for the given image to be used on an educational website. --- **Identifying Graphs of the Function \( f(x) \)** The image below contains four different graphs (A, B, C, and D) of a function \( f(x) \). Your task is to analyze each graph and determine their characteristics. ### Graph A: ![Graph A](https://example.com/image1.png) - The graph shows a sinusoidal wave with peaks and troughs. - It intersects the x-axis at \(0, \pi, 2\pi,\)..., and so on. - It has a maximum value above 2 and a minimum value below -2 across one period. - The x-axis labels include fractions of \(\pi\): \( \frac{-3\pi}{2}, -\pi, \frac{-\pi}{2}, 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \). ### Graph B: ![Graph B](https://example.com/image2.png) - The graph presents a sinusoidal wave, similar to Graph A but with a lesser amplitude. - The peaks and troughs barely touch above 2 and below -2 across one period. - It intersects the x-axis at the same points as Graph A. - Clearly visible x-axis labels include: \( \frac{-3\pi}{2}, -\pi, \frac{-\pi}{2}, 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \). ### Graph C: ![Graph C](https://example.com/image3.png) - This graph illustrates a smooth wave-like function with smaller amplitude. - The maximum and minimum values do not reach the values achieved in Graph A or B. - The x-axis intersections remain consistent with labels: \( \frac{-3\pi}{2}, -\pi, \frac{-\pi}{2}, 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \). ### Graph D: ![Graph D](https://example.com/image4.png) - The final graph depicts a sinusoidal wave with peaks and troughs similar to the previous graphs. - It also intersects the x-axis at \(0, \pi, 2\pi,\)..., and so on. - The amplitude appears comparable to Graph B
Transcribed Image Text:Here is a transcription and detailed explanation for the given image to be used on an educational website. --- **Identifying Graphs of the Function \( f(x) \)** The image below contains four different graphs (A, B, C, and D) of a function \( f(x) \). Your task is to analyze each graph and determine their characteristics. ### Graph A: ![Graph A](https://example.com/image1.png) - The graph shows a sinusoidal wave with peaks and troughs. - It intersects the x-axis at \(0, \pi, 2\pi,\)..., and so on. - It has a maximum value above 2 and a minimum value below -2 across one period. - The x-axis labels include fractions of \(\pi\): \( \frac{-3\pi}{2}, -\pi, \frac{-\pi}{2}, 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \). ### Graph B: ![Graph B](https://example.com/image2.png) - The graph presents a sinusoidal wave, similar to Graph A but with a lesser amplitude. - The peaks and troughs barely touch above 2 and below -2 across one period. - It intersects the x-axis at the same points as Graph A. - Clearly visible x-axis labels include: \( \frac{-3\pi}{2}, -\pi, \frac{-\pi}{2}, 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \). ### Graph C: ![Graph C](https://example.com/image3.png) - This graph illustrates a smooth wave-like function with smaller amplitude. - The maximum and minimum values do not reach the values achieved in Graph A or B. - The x-axis intersections remain consistent with labels: \( \frac{-3\pi}{2}, -\pi, \frac{-\pi}{2}, 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2} \). ### Graph D: ![Graph D](https://example.com/image4.png) - The final graph depicts a sinusoidal wave with peaks and troughs similar to the previous graphs. - It also intersects the x-axis at \(0, \pi, 2\pi,\)..., and so on. - The amplitude appears comparable to Graph B
**Select the correct answer.** The parent cosine function is transformed to create the function \( m(x) = -2\cos(x + \pi) \). Which graphed function has the same amplitude as function \( m \)? - **A.** - A graph of \( f(x) \) against \( x \) is shown. The graph has a cosine wave that starts at \((-\frac{3\pi}{2}, 0)\), rises to a maximum of 2 at \( x = -\pi \), falls to a minimum of -2 at \( x = 0 \), rises to a maximum of 2 at \( x = \pi \), and then falls to 0 at \((\frac{3\pi}{2}, 0)\). The amplitude of this function is 2. - **B.** - A graph of \( f(x) \) against \( x \) is shown. The graph has a cosine wave that starts at \((-\frac{3\pi}{2}, 2)\), falls through 0 at \( x = -\pi \), reaches a minimum of -2 at \( x = -\frac{\pi}{2} \), rises through 0 at \( x = 0 \), reaches a maximum of 2 at \( x = \frac{\pi}{2} \), falls through 0 at \( x = \pi \), and then rises to 2 at \((\frac{3\pi}{2}, 0)\). The amplitude of this function is 2. - **C.** - A graph of \( f(x) \) against \( x \) is shown. The graph has a cosine wave that starts at \((-\frac{3\pi}{2}, -1)\), rises to a maximum of 1 at \( x = -\pi \), falls to a minimum of -1 at \( x = 0 \), rises to a maximum of 1 at \( x = \pi \), and then falls to -1 at \((\frac{3\pi}{2}, -1)\). The amplitude of this function is 1. **Correct Answer: B** - B is correct because the graph of \( f(x) \) has an amplitude of 2, which matches the amplitude of the transformed function \( m(x) = -2\cos(x + \pi
Transcribed Image Text:**Select the correct answer.** The parent cosine function is transformed to create the function \( m(x) = -2\cos(x + \pi) \). Which graphed function has the same amplitude as function \( m \)? - **A.** - A graph of \( f(x) \) against \( x \) is shown. The graph has a cosine wave that starts at \((-\frac{3\pi}{2}, 0)\), rises to a maximum of 2 at \( x = -\pi \), falls to a minimum of -2 at \( x = 0 \), rises to a maximum of 2 at \( x = \pi \), and then falls to 0 at \((\frac{3\pi}{2}, 0)\). The amplitude of this function is 2. - **B.** - A graph of \( f(x) \) against \( x \) is shown. The graph has a cosine wave that starts at \((-\frac{3\pi}{2}, 2)\), falls through 0 at \( x = -\pi \), reaches a minimum of -2 at \( x = -\frac{\pi}{2} \), rises through 0 at \( x = 0 \), reaches a maximum of 2 at \( x = \frac{\pi}{2} \), falls through 0 at \( x = \pi \), and then rises to 2 at \((\frac{3\pi}{2}, 0)\). The amplitude of this function is 2. - **C.** - A graph of \( f(x) \) against \( x \) is shown. The graph has a cosine wave that starts at \((-\frac{3\pi}{2}, -1)\), rises to a maximum of 1 at \( x = -\pi \), falls to a minimum of -1 at \( x = 0 \), rises to a maximum of 1 at \( x = \pi \), and then falls to -1 at \((\frac{3\pi}{2}, -1)\). The amplitude of this function is 1. **Correct Answer: B** - B is correct because the graph of \( f(x) \) has an amplitude of 2, which matches the amplitude of the transformed function \( m(x) = -2\cos(x + \pi
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