3x +4, x<-2 Graph and label the function: g(x)={5, x =-2 |-x+1, 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...
Question
**Graph and Label the Function**

Given the piecewise function \( g(x) \):

\[
g(x) = 
\begin{cases} 
3x + 4, & x < -2 \\
5, & x = -2 \\
-x + 1, & x > -2 
\end{cases}
\]

### Explanation:

- **For \( x < -2 \):** The function is defined as \( g(x) = 3x + 4 \). This is a linear equation with a slope of 3 and a y-intercept of 4.

- **At \( x = -2 \):** The function takes on a constant value, \( g(x) = 5 \). This represents a single point on the graph at (-2, 5).

- **For \( x > -2 \):** The function is \( g(x) = -x + 1 \). This is also a linear equation, but with a slope of -1 and a y-intercept of 1.

When graphing, ensure to:

1. Plot the line \( 3x + 4 \) for all x-values less than -2.
2. Mark the point (-2, 5) on the graph, representing the value of the function at \( x = -2 \).
3. Plot the line \(-x + 1\) for all x-values greater than -2.

Use open and closed circles as necessary to indicate whether endpoints are included in each piece of the function.
Transcribed Image Text:**Graph and Label the Function** Given the piecewise function \( g(x) \): \[ g(x) = \begin{cases} 3x + 4, & x < -2 \\ 5, & x = -2 \\ -x + 1, & x > -2 \end{cases} \] ### Explanation: - **For \( x < -2 \):** The function is defined as \( g(x) = 3x + 4 \). This is a linear equation with a slope of 3 and a y-intercept of 4. - **At \( x = -2 \):** The function takes on a constant value, \( g(x) = 5 \). This represents a single point on the graph at (-2, 5). - **For \( x > -2 \):** The function is \( g(x) = -x + 1 \). This is also a linear equation, but with a slope of -1 and a y-intercept of 1. When graphing, ensure to: 1. Plot the line \( 3x + 4 \) for all x-values less than -2. 2. Mark the point (-2, 5) on the graph, representing the value of the function at \( x = -2 \). 3. Plot the line \(-x + 1\) for all x-values greater than -2. Use open and closed circles as necessary to indicate whether endpoints are included in each piece of the function.
Expert Solution
Step 1

Given function

g(x) = 3x+4,x<-25,x=-2-x+1,x>-2

steps

Step by step

Solved in 3 steps with 1 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