Chapter 4.6, Problem 33E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Analyzing the Graph of a Function In Exercises 5-54, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = | 2 x − 3 |

To determine

To graph: The function y=|2x3|.

Explanation

Given:

y=|2xâˆ’3|

Graph:

The function has a domain as (âˆ’âˆž,âˆž).

The function can never take a negative value and thus has a range as [0,âˆž).

Now find the x and y intercepts by equating f(x) and x to zero respectively to obtain:

The x-intercept is (1.5,0) and the y-intercept is (0,3).

The function is defined for all real numbers and also as a linear modulus function has no horizontal or vertical asymptotes.

Now equate the derivative of the function to zero to get the critical points.

y'(x)=4xâˆ’6|2xâˆ’3|

This derivative is undefined at x=1.5 and thus this would be a critical number.

The critical number gives two test intervals (âˆ’âˆž,1.5),(1.5,âˆž).

Let 0âˆˆ(âˆ’âˆž,1.5).

y'(0)=4(0)âˆ’6|2(0)âˆ’3|=âˆ’63<0

Hence, the function is decreasing in this interval

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Sketch the region bounded by the curves. 33. y = 3x, y = x2

Single Variable Calculus: Early Transcendentals, Volume I

#### What is the slope of a nonvertical line? What can you say about the slope of a vertical line?

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problems 45-51, solve each system of equations. 49.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: The domain is all numbers x for which f(x) is defined.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Multivariable Calculus, 8th

#### Find each value. P(7,2)

College Algebra (MindTap Course List)