Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Chapter 3.8, Problem 24PPS
To determine

To graph the function g(x)=|3x| and determine its domain and range and its relation with the graph of the function f(x)=|x| .

Expert Solution & Answer
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Answer to Problem 24PPS

Domain: x

Range: y[0,)

Explanation of Solution

Given:

Function: g(x)=|3x|

Concept used:

The general form of an absolute value function is f(x)=a|xh|+k .

The graph of f(x)=a|xh|+k is a “V” with vertex (h,k) , slope m=a on the right side of the vertex (x>h) and slope m=a on the left side of the vertex (x<h) . The graph of f(x)=a|xh|+k is an upside-down “V” with vertex (h,k) , slope m=a for (x>h) and slope m=a for (x<h) .

Calculation for graph:

Consider g(x)=|3x|=3|x|,

Compare with the general form:

  g(x)=a|xh|+k

Here, the value of a=3 , so the graph opens upwards with a slope of 3 .

The value of h=0 and the value of k=0 , so the vertex of the graph is (0,0) .

    Values of x Values of g (x)
    0 0
    1 3
    -1

      3

    2 6
    -2 6

By taking different values of x , the graph can be plotted.

Graph:

The graph of g(x)=|3x| :

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 3.8, Problem 24PPS , additional homework tip  1

Interpretation:

From the graph, it can be observed that the horizontal extent of the graph is from to , so the domain of g(x) is (,) .

The vertical extent of the graph is from 0 to , so the range of g(x) is [0,) .

Comparison:

Now, comparing the graph of g(x) with the graph of f(x)=|x| .

Graph of f(x)=|x|

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 3.8, Problem 24PPS , additional homework tip  2

The vertex, domain and range of both the graphs are (0,0) , (,) and [0,) respectively.

Therefore, both the graphs have same vertex, same domain and same range.

Conclusion:

Therefore, the domain of g(x)=|3x| is x and range is y[0,) .

Chapter 3 Solutions

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Ch. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42PPSCh. 3.1 - Prob. 43PPSCh. 3.1 - Prob. 44PPSCh. 3.1 - Prob. 45PPSCh. 3.1 - Prob. 46PPSCh. 3.1 - Prob. 47PPSCh. 3.1 - Prob. 48PPSCh. 3.1 - Prob. 49PPSCh. 3.1 - 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Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY