/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 87 Begin by graphing the absolute v... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 87

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$h(x)=-|x+4|$$

Short Answer

Expert verified
The solution graph of the function \(h(x)= -|x+4|\) is a v-shaped curve that opens downwards (due to the negative absolute value) and is shifted 4 units left from the origin.

Step by step solution

01

Graph of Absolute Value Function

To begin, a basic understanding of the absolute value function is needed. To graph the absolute function \(f(x)=|x|\), note that the absolute value of \(x\) makes the output nonnegative. The resulting graph is a V shape which intersects the origin (0,0) and opens upwards because all values of \(x\) are positive or zero.
02

Translate and Reflect function

The function \(h(x)=-|x+4|\) is a transformation of the absolute value function. This function can be obtained by shifting the function \(|x|\) to the left by 4 units and then reflecting it about the x-axis by multiplying it by -1. So, move all points on the \(|x|\) graph to the left by 4 units and then flip it over the x-axis. Ensure to change only the x-coordinates of the graph by subtracting 4 from them, then change all y-coordinates to their opposite value (if positive, make them negative), thus obtaining the graph for the function \(h(x)=-|x+4|\).
03

Validate the Graph

Ensure your final graph has been moved to the left by 4 units relative to the original graph and is opening downwards. You can validate the graph accuracy by checking a few key points. For example, input x = 0 into \(h(x)=-|x+4|\), gets h(0) = -4, meaning the point (0, -4) should be on your graph. This way you can verify that the transformations were done correctly.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-4 x-12 y-9=0$$

Will help you prepare for the material covered in the next section. Find the ordered pairs \((\quad, 0)\) and \((0, \quad)\) satisfying \(4 x-3 y-6=0\).

In your own words, describe how to find the distance between two points in the rectangular coordinate system.

Explaining the Concepts: If a function is defined by an equation, explain how to find its domain.

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{\frac{1}{3}}(x-4)$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.