/*! 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 89 Begin by graphing the absolute v... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 89

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$g(x)=-|x+4|+1$$

Short Answer

Expert verified
The function \(g(x)=-|x+4|+1\) is a transformation of the base function \(f(x)=|x|\). It's graph is a V-shaped graph reflected over the x-axis, shifted 4 units to the left and 1 unit upwards with the vertex at (-4,1).

Step by step solution

01

Graphing the base function

Plot the function \(f(x)=|x|\). This is a V-shaped graph, where the vertex is at the origin (0,0) and the lines y=x for x>=0 and y=-x for x<0 form the arms of the 'v'.
02

Applying transformations to the base function

The function \(g(x)=-|x+4|+1\) represents a transformation of the base function \(f(x)=|x|\). The '+4' inside the absolute value symbol translates the graph 4 units to the left. The '-' sign in front of the absolute value symbol reflects the graph over the x-axis. Lastly, the '+1' outside the absolute value symbol translates the graph 1 unit upward.
03

Graph the transformed function

Using the transformations interpreted in Step 2, graph the given function \(g(x)=-|x+4|+1\). The vertex of this function will be (-4,1). The left arm of the 'v' (for x<-4) will be the line y=-(x+4)+1. The right arm of the 'v' (for x>=-4) will be the line y=(x+4)+1. The function should be reflected over the x-axis and shifted 4 units to the left and 1 unit upwards compared to the base function graph.

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

I noticed that the difference quotient is always zero if \(f(x)=c,\) where \(c\) is any constant.

Explaining the Concepts: If equations for two functions are given, explain how to obtain the quotient function and its domain.

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-x+2 y+1=0$$

I graphed $$f(x)=\left\\{\begin{array}{lll} 2 & \text { if } & x \neq 4 \\ 3 & \text { if } & x=4 \end{array}\right.$$ and one piece of my graph is a single point.

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

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Calculus

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.