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**Text Transcription:** "The function graphed is of the form \( y = a \tan bx \) or \( y = a \cot bx \), where \( b > 0 \). Determine the equation of the graph." **Graph Explanation:** The graph displays a trigonometric function plotted on a coordinate plane. Key features include: - The y-axis is marked with significant values, with a visible point at \( y = 5 \). - The x-axis shows key increments, including labels at \( -\frac{3\pi}{2} \) and \( \frac{3\pi}{2} \). - Vertical asymptotes are present at \( x = -\frac{3\pi}{2} \) and \( x = \frac{3\pi}{2} \), indicating where the function is undefined. - The curves of the function slope upwards in between and beyond these asymptotes, characteristic of a tangent function. - The pattern suggests periodicity, typical in trigonometric graphs, with intervals repeating every \( \pi \) units along the x-axis. To determine the equation from the form \( y = a \tan bx \) or \( y = a \cot bx \), observe aspects such as the period and vertical stretch. The image displays a coordinate plane with a graph depicting several hyperbolic curves. The x-axis is labeled with increments showing \(-\frac{3\pi}{2}\) on the left and \(\frac{3\pi}{2}\) on the right. The y-axis is marked with values reaching from -5 to 5. Both axes feature arrows indicating the graph extends indefinitely in all directions. The hyperbolic curves illustrate sections of the tangent or cotangent function, with vertical asymptotes occurring at the labels on the x-axis. These curves are symmetric around the origin and appear to approach the vertical asymptotes while extending infinitely along the vertical direction.

**Text Transcription:** "The function graphed is of the form \( y = a \tan bx \) or \( y = a \cot bx \), where \( b > 0 \). Determine the equation of the graph." **Graph Explanation:** The graph displays a trigonometric function plotted on a coordinate plane. Key features include: - The y-axis is marked with significant values, with a visible point at \( y = 5 \). - The x-axis shows key increments, including labels at \( -\frac{3\pi}{2} \) and \( \frac{3\pi}{2} \). - Vertical asymptotes are present at \( x = -\frac{3\pi}{2} \) and \( x = \frac{3\pi}{2} \), indicating where the function is undefined. - The curves of the function slope upwards in between and beyond these asymptotes, characteristic of a tangent function. - The pattern suggests periodicity, typical in trigonometric graphs, with intervals repeating every \( \pi \) units along the x-axis. To determine the equation from the form \( y = a \tan bx \) or \( y = a \cot bx \), observe aspects such as the period and vertical stretch. The image displays a coordinate plane with a graph depicting several hyperbolic curves. The x-axis is labeled with increments showing \(-\frac{3\pi}{2}\) on the left and \(\frac{3\pi}{2}\) on the right. The y-axis is marked with values reaching from -5 to 5. Both axes feature arrows indicating the graph extends indefinitely in all directions. The hyperbolic curves illustrate sections of the tangent or cotangent function, with vertical asymptotes occurring at the labels on the x-axis. These curves are symmetric around the origin and appear to approach the vertical asymptotes while extending infinitely along the vertical direction.

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Text Transcription:** "The function graphed is of the form \( y = a \tan bx \) or \( y = a \cot bx \), where \( b > 0 \). Determine the equation of the graph." **Graph Explanation:** The graph displays a trigonometric function plotted on a coordinate plane. Key features include: - The y-axis is marked with significant values, with a visible point at \( y = 5 \). - The x-axis shows key increments, including labels at \( -\frac{3\pi}{2} \) and \( \frac{3\pi}{2} \). - Vertical asymptotes are present at \( x = -\frac{3\pi}{2} \) and \( x = \frac{3\pi}{2} \), indicating where the function is undefined. - The curves of the function slope upwards in between and beyond these asymptotes, characteristic of a tangent function. - The pattern suggests periodicity, typical in trigonometric graphs, with intervals repeating every \( \pi \) units along the x-axis. To determine the equation from the form \( y = a \tan bx \) or \( y = a \cot bx \), observe aspects such as the period and vertical stretch.
Transcribed Image Text:**Text Transcription:** "The function graphed is of the form \( y = a \tan bx \) or \( y = a \cot bx \), where \( b > 0 \). Determine the equation of the graph." **Graph Explanation:** The graph displays a trigonometric function plotted on a coordinate plane. Key features include: - The y-axis is marked with significant values, with a visible point at \( y = 5 \). - The x-axis shows key increments, including labels at \( -\frac{3\pi}{2} \) and \( \frac{3\pi}{2} \). - Vertical asymptotes are present at \( x = -\frac{3\pi}{2} \) and \( x = \frac{3\pi}{2} \), indicating where the function is undefined. - The curves of the function slope upwards in between and beyond these asymptotes, characteristic of a tangent function. - The pattern suggests periodicity, typical in trigonometric graphs, with intervals repeating every \( \pi \) units along the x-axis. To determine the equation from the form \( y = a \tan bx \) or \( y = a \cot bx \), observe aspects such as the period and vertical stretch.
The image displays a coordinate plane with a graph depicting several hyperbolic curves. The x-axis is labeled with increments showing \(-\frac{3\pi}{2}\) on the left and \(\frac{3\pi}{2}\) on the right. The y-axis is marked with values reaching from -5 to 5. Both axes feature arrows indicating the graph extends indefinitely in all directions. The hyperbolic curves illustrate sections of the tangent or cotangent function, with vertical asymptotes occurring at the labels on the x-axis. These curves are symmetric around the origin and appear to approach the vertical asymptotes while extending infinitely along the vertical direction.
Transcribed Image Text:The image displays a coordinate plane with a graph depicting several hyperbolic curves. The x-axis is labeled with increments showing \(-\frac{3\pi}{2}\) on the left and \(\frac{3\pi}{2}\) on the right. The y-axis is marked with values reaching from -5 to 5. Both axes feature arrows indicating the graph extends indefinitely in all directions. The hyperbolic curves illustrate sections of the tangent or cotangent function, with vertical asymptotes occurring at the labels on the x-axis. These curves are symmetric around the origin and appear to approach the vertical asymptotes while extending infinitely along the vertical direction.
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