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What are the equations for the vertical and horizontal asymptotes?

What are the equations for the vertical and horizontal asymptotes?

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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What are the equations for the vertical and horizontal asymptotes?
The image shows a graph of a parabola on a coordinate plane. ### Description: - **Axes:** - The horizontal axis is labeled as the x-axis. - The vertical axis is labeled as the y-axis. - Both axes are marked with increments of 1, with grid lines at every 1 unit. - **Parabola:** - The graph displays a parabola opening upwards. - The vertex of the parabola appears to be at the origin (0,0), but due to lack of explicit markings, this is assumed from symmetry. - As the parabola is symmetric with respect to the y-axis, the shape is balanced on both sides of the y-axis. - **Range and Domain:** - The x-axis extends from -10 to 10. - The y-axis extends from -10 to 10. - **Grid and Guidelines:** - The background consists of a grid that helps to measure and understand the scale and position of the parabola relative to the axes. This graph is useful for understanding the basic structure of a quadratic function and its properties such as symmetry and the concept of a vertex.
Transcribed Image Text:The image shows a graph of a parabola on a coordinate plane. ### Description: - **Axes:** - The horizontal axis is labeled as the x-axis. - The vertical axis is labeled as the y-axis. - Both axes are marked with increments of 1, with grid lines at every 1 unit. - **Parabola:** - The graph displays a parabola opening upwards. - The vertex of the parabola appears to be at the origin (0,0), but due to lack of explicit markings, this is assumed from symmetry. - As the parabola is symmetric with respect to the y-axis, the shape is balanced on both sides of the y-axis. - **Range and Domain:** - The x-axis extends from -10 to 10. - The y-axis extends from -10 to 10. - **Grid and Guidelines:** - The background consists of a grid that helps to measure and understand the scale and position of the parabola relative to the axes. This graph is useful for understanding the basic structure of a quadratic function and its properties such as symmetry and the concept of a vertex.
Expert Solution
Step 1: Given and Concept

A graph is provided with one horizontal line and two vertical lines along with the curves.

The objective is to write the equations of the horizontal and vertical asymptotes.

Concept used:

Horizontal Asymptote:

When x rightwards arrow plus-or-minus infinity, the curve approaches some constant value b comma and is called a Horizontal Asymptote.

The curve y equals f open parentheses x close parentheses never touches the value y equals b. 

Then, the equation y equals b is the equation of horizontal asymptote.

Vertical Asymptote:

When x rightwards arrow a, the curve approaches plus-or-minus infinity and is called a Vertical Asymptote.

The curve y equals f open parentheses x close parentheses never assumes the value for x equals a. 

Then, the equation x equals a is the equation of vertical asymptote.

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