-4-3-2 VA 3 2 1-2 x = – 1 y = 1 3 4 5 x x = 2

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...
icon
Related questions
Question

I need help finding a equation that fits this graph.

The image is a graph depicting the function \( f(x) \) with vertical and horizontal asymptotes, as well as significant points marked on the Cartesian plane. Below is a detailed description:

- **Axes:**
  - The horizontal axis is labeled as the \( x \)-axis.
  - The vertical axis is labeled as the \( y \)-axis.

- **Asymptotes:**
  - A vertical asymptote is drawn as a dashed pink line at \( x = -1 \).
  - Another vertical asymptote is drawn as a dashed pink line at \( x = 2 \).
  - A horizontal asymptote is placed at \( y = 1 \) with a dashed pink line.

- **Curve:**
  - The curve approaches the vertical asymptote at \( x = -1 \) from both sides.
  - The curve descends towards the asymptote at \( x = 2 \) and moves away on the other side.
  - There is a smooth transition just below the horizontal asymptote \( y = 1 \) as \( x \) increases.

- **Labeled Points:**
  - Points along the \( x \)-axis are labeled at intervals: \(-4, -3, -2, 1, 3, 4, 5\).
  - Points along the \( y \)-axis are labeled at values: \(-2, -1, 1, 2, 3\).

The overall behavior illustrated is typical of a rational function involving vertical and horizontal asymptotes, showing two branches of the curve that approach the asymptotes yet do not intersect them.
Transcribed Image Text:The image is a graph depicting the function \( f(x) \) with vertical and horizontal asymptotes, as well as significant points marked on the Cartesian plane. Below is a detailed description: - **Axes:** - The horizontal axis is labeled as the \( x \)-axis. - The vertical axis is labeled as the \( y \)-axis. - **Asymptotes:** - A vertical asymptote is drawn as a dashed pink line at \( x = -1 \). - Another vertical asymptote is drawn as a dashed pink line at \( x = 2 \). - A horizontal asymptote is placed at \( y = 1 \) with a dashed pink line. - **Curve:** - The curve approaches the vertical asymptote at \( x = -1 \) from both sides. - The curve descends towards the asymptote at \( x = 2 \) and moves away on the other side. - There is a smooth transition just below the horizontal asymptote \( y = 1 \) as \( x \) increases. - **Labeled Points:** - Points along the \( x \)-axis are labeled at intervals: \(-4, -3, -2, 1, 3, 4, 5\). - Points along the \( y \)-axis are labeled at values: \(-2, -1, 1, 2, 3\). The overall behavior illustrated is typical of a rational function involving vertical and horizontal asymptotes, showing two branches of the curve that approach the asymptotes yet do not intersect them.
Expert Solution
Step 1: Write what is given and what to find

Calculus homework question answer, step 1, image 1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning