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For the graph below, give a restricted domain that includes x = = 0 and the entire range of the function. -5 -4 -3 -2 -1 A 3 2 N 41 -2 -3 -4 -5- 1 2 3 بنا Git 4 5 o

For the graph below, give a restricted domain that includes x = = 0 and the entire range of the function. -5 -4 -3 -2 -1 A 3 2 N 41 -2 -3 -4 -5- 1 2 3 بنا Git 4 5 o

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Transcription:** For the graph below, give a restricted domain that includes \( x = 0 \) and the entire range of the function. **Graph Explanation:** The graph displays the tangent function \( y = \tan(x) \), which has asymptotes and is periodic. The graph consists of several upward-sloping curves separated by vertical asymptotes. - **X-Axis (Horizontal):** Labeled from -5 to 5 with major grid lines at every integer. - **Y-Axis (Vertical):** Labeled from -5 to 5 with major grid lines at every integer. **Details:** - The tangent function has vertical asymptotes where the function is undefined, occurring at \( x = \frac{\pi}{2} + n\pi \) for integers \( n \). - In this particular view, at least three segments of the tangent function are visible between vertical asymptotes. - The segment directly centered through the y-axis occurs between \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \). - Within each segment, the function increases from negative to positive infinity. The task is to determine a restricted domain that includes \( x = 0 \) while capturing the full range of the function, which is all real numbers from negative to positive infinity.
Transcribed Image Text:**Transcription:** For the graph below, give a restricted domain that includes \( x = 0 \) and the entire range of the function. **Graph Explanation:** The graph displays the tangent function \( y = \tan(x) \), which has asymptotes and is periodic. The graph consists of several upward-sloping curves separated by vertical asymptotes. - **X-Axis (Horizontal):** Labeled from -5 to 5 with major grid lines at every integer. - **Y-Axis (Vertical):** Labeled from -5 to 5 with major grid lines at every integer. **Details:** - The tangent function has vertical asymptotes where the function is undefined, occurring at \( x = \frac{\pi}{2} + n\pi \) for integers \( n \). - In this particular view, at least three segments of the tangent function are visible between vertical asymptotes. - The segment directly centered through the y-axis occurs between \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \). - Within each segment, the function increases from negative to positive infinity. The task is to determine a restricted domain that includes \( x = 0 \) while capturing the full range of the function, which is all real numbers from negative to positive infinity.
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