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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Differential Equations
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Chapter 3.8, Problem 35PPS

a.

To determine

To make the table of values for the function f(x)=|2x+3|.

a.

Expert Solution
Check Mark

Explanation of Solution

Given:

Function: f(x)=|2x+3|

Calculation:

Consider f(x)=|2x+3|

    Values of x Values of f (x)
    −57
    −45
    −33
    −21
    −11
    0 3
    1 5
    27
    39
    411
    513

b.

To determine

To plot the points obtained in (a) on a coordinate grid.

b.

Expert Solution
Check Mark

Explanation of Solution

Given:

Table in subpart (a) of the function f(x)=|2x+3| .

Graph:

Consider the table in (a).

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 3.8, Problem 35PPS , additional homework tip 1

c.

To determine

To graph the given function f(x)=|2x+3|

c.

Expert Solution
Check Mark

Explanation of Solution

Given:

Function: f(x)=|2x+3|

Concept used:

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

The graph of f(x)=a|x−h|+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|x−h|+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 f(x)=|2x+3|=2|x+32|

Compare with the general form:

  g(x)=a|x−h|+k

Here, the value of a=2 , so the graph opens upwards with a slope of 2 .

The value of h=−32 and the value of k=0 , so the vertex of the graph is (−32,0).

    Values of x Values of f (x)
    −57
    −45
    −33
    −21
    −11
    0 3
    1 5
    27
    39
    411
    513

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

Graph:

The graph of f(x)=|2x+3| :

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 3.8, Problem 35PPS , additional homework tip 2

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,∞) .

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Chapter 3.8, Problem 34PPS
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Chapter 3.8, Problem 36PPS

Chapter 3 Solutions

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

Ch. 3.1 - Prob. 1AGPCh. 3.1 - Prob. 1BGPCh. 3.1 - Prob. 2GPCh. 3.1 - Prob. 3GPCh. 3.1 - Prob. 4AGPCh. 3.1 - Prob. 4BGPCh. 3.1 - Prob. 5AGPCh. 3.1 - Prob. 5BGPCh. 3.1 - Prob. 5CGPCh. 3.1 - Prob. 1CYU
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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