Homework Help is Here – Start Your Trial Now!
Math
Calculus
(a) Graph f(x) = 3 x for x < 0. (b) Graph g(x) = 2√√x for x ≥ 0. (c) Graph r(x) = 3|x for x < 0 2√x for x ≥0

(a) Graph f(x) = 3 x for x < 0. (b) Graph g(x) = 2√√x for x ≥ 0. (c) Graph r(x) = 3|x for x < 0 2√x for x ≥0

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...
See similar textbooks
icon
Related questions
Question
## Graphical Functions and Their Domain ### (a) Graph of \( f(x) = 3|x| \) for \( x < 0 \) This function represents a linear relationship between the variables \( f(x) \) and \( x \) with a slope of 3. The absolute value ensures positive values for \( |x| \). However, the domain specified is only for negative values of \( x \) (i.e., \( x < 0 \)). ### (b) Graph of \( g(x) = 2\sqrt{x} \) for \( x \geq 0 \) This function indicates a square root relationship between \( g(x) \) and \( x \), scaled by a factor of 2. The domain for this function is restricted to non-negative values of \( x \) (i.e., \( x \geq 0 \)). ### (c) Graph of \( r(x) \) \[ r(x) = \begin{cases} 3|x| & \text{for } x<0 \\ 2\sqrt{x} & \text{for } x \geq 0 \end{cases} \] This piecewise function merges the two previously defined graphs, specifying: - \( 3|x| \) for negative values of \( x \) (i.e., \( x < 0 \)). - \( 2\sqrt{x} \) for non-negative values of \( x \) (i.e., \( x \geq 0 \)). This results in a composite graph where the left side (for negative \( x \)) follows a linear pattern with a slope of 3, and the right side (for non-negative \( x \)) follows a square root relationship scaled by 2.
Transcribed Image Text:## Graphical Functions and Their Domain ### (a) Graph of \( f(x) = 3|x| \) for \( x < 0 \) This function represents a linear relationship between the variables \( f(x) \) and \( x \) with a slope of 3. The absolute value ensures positive values for \( |x| \). However, the domain specified is only for negative values of \( x \) (i.e., \( x < 0 \)). ### (b) Graph of \( g(x) = 2\sqrt{x} \) for \( x \geq 0 \) This function indicates a square root relationship between \( g(x) \) and \( x \), scaled by a factor of 2. The domain for this function is restricted to non-negative values of \( x \) (i.e., \( x \geq 0 \)). ### (c) Graph of \( r(x) \) \[ r(x) = \begin{cases} 3|x| & \text{for } x<0 \\ 2\sqrt{x} & \text{for } x \geq 0 \end{cases} \] This piecewise function merges the two previously defined graphs, specifying: - \( 3|x| \) for negative values of \( x \) (i.e., \( x < 0 \)). - \( 2\sqrt{x} \) for non-negative values of \( x \) (i.e., \( x \geq 0 \)). This results in a composite graph where the left side (for negative \( x \)) follows a linear pattern with a slope of 3, and the right side (for non-negative \( x \)) follows a square root relationship scaled by 2.
Expert Solution
steps

Step by step

Solved in 4 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
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
SEE MORE TEXTBOOKS