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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Identify the asymptotes in the displayed domain of the graph you selected above. (Enter your answers as a comma-separated list of equations.)
please help me find the correct answer, I had previously asked this question and got the answer: 1, 5, −3, −5 but it is wrong. (please help me understand why)
![The given mathematical function is:
\[ h(x) = 8 \sec \left( \frac{\pi}{4}(x + 1) \right) \]
This function involves the secant trigonometric function, which is the reciprocal of the cosine function. The expression inside the secant function is a linear transformation of \( x \). The transformation includes a horizontal shift of \( -1 \) and a horizontal stretch by a factor of \( \frac{4}{\pi} \). The \( 8 \) outside the secant function acts as a vertical stretch.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc41bfb8-15a9-422f-9963-f8c641630ea0%2F7f45bcf6-4f5f-43ae-acd7-01e25d4a996b%2Fi4oiar_processed.png&w=3840&q=75)
Transcribed Image Text:The given mathematical function is:
\[ h(x) = 8 \sec \left( \frac{\pi}{4}(x + 1) \right) \]
This function involves the secant trigonometric function, which is the reciprocal of the cosine function. The expression inside the secant function is a linear transformation of \( x \). The transformation includes a horizontal shift of \( -1 \) and a horizontal stretch by a factor of \( \frac{4}{\pi} \). The \( 8 \) outside the secant function acts as a vertical stretch.
Transcribed Image Text:The image displays the graph of the function \(y = \frac{1}{x^2}\). This graph consists of symmetrical curves with respect to the y-axis, and it's defined for all \(x \neq 0\).
### Detailed Explanation:
- **Graph Behavior:**
- As \(x\) approaches 0 from the positive or negative side, \(y\) approaches infinity. This describes a vertical asymptote along the y-axis.
- As \(x\) moves away from zero, in both positive and negative directions, the value of \(y\) decreases and approaches zero, but never actually reaches zero.
- **Axes and Scales:**
- The x-axis is labeled with intervals from -8 to 8.
- The y-axis is labeled with intervals from -16 to 16.
- **Quadrants:**
- The graph is shown in the first and second quadrants since the function produces positive \(y\)-values for any real \(x\).
This graph helps in understanding the behavior of reciprocal functions and their properties, such as asymptotes and symmetry.
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