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shown? 8 Oy = 4 y = 2 O O x = 2 x = 4 -4 ILIUIT TUE y₁ 8 0 4 n -8 I L I I I I 4 8 te of the gr

shown? 8 Oy = 4 y = 2 O O x = 2 x = 4 -4 ILIUIT TUE y₁ 8 0 4 n -8 I L I I I I 4 8 te of the gr

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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### Understanding Horizontal Asymptotes **Question:** What is the equation for the horizontal asymptote of the graph of the function shown? **Graph Illustration:** The provided graph displays a function along with its asymptotes on the Cartesian plane. - **X-Axis Range:** -8 to 8 - **Y-Axis Range:** -8 to 8 The graph depicts two asymptotes: 1. **Vertical Asymptote at \( x = 0 \)** (dashed vertical line). 2. **Horizontal Asymptote at \( y = 4 \)** (dashed horizontal line). The curve approaches these asymptotes but never intersects them. **Multiple Choice Options:** - \( \circ \) \( y = 4 \) - \( \circ \) \( y = 2 \) - \( \circ \) \( x = 2 \) - \( \circ \) \( x = 4 \) **Answer Explanation:** To determine the horizontal asymptote, observe the behavior of the function as \( x \) approaches positive or negative infinity. The graph clearly shows that the function approaches the line \( y = 4 \). **Correct Answer:** \( \bullet \) \( y = 4 \) This indicates that as \( x \) moves towards positive or negative infinity, the value of \( y \) gets closer and closer to 4, making \( y = 4 \) the horizontal asymptote of the function.
Transcribed Image Text:### Understanding Horizontal Asymptotes **Question:** What is the equation for the horizontal asymptote of the graph of the function shown? **Graph Illustration:** The provided graph displays a function along with its asymptotes on the Cartesian plane. - **X-Axis Range:** -8 to 8 - **Y-Axis Range:** -8 to 8 The graph depicts two asymptotes: 1. **Vertical Asymptote at \( x = 0 \)** (dashed vertical line). 2. **Horizontal Asymptote at \( y = 4 \)** (dashed horizontal line). The curve approaches these asymptotes but never intersects them. **Multiple Choice Options:** - \( \circ \) \( y = 4 \) - \( \circ \) \( y = 2 \) - \( \circ \) \( x = 2 \) - \( \circ \) \( x = 4 \) **Answer Explanation:** To determine the horizontal asymptote, observe the behavior of the function as \( x \) approaches positive or negative infinity. The graph clearly shows that the function approaches the line \( y = 4 \). **Correct Answer:** \( \bullet \) \( y = 4 \) This indicates that as \( x \) moves towards positive or negative infinity, the value of \( y \) gets closer and closer to 4, making \( y = 4 \) the horizontal asymptote of the function.
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