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 54HP
To determine

To determine the function from the given graph.

Expert Solution & Answer
Check Mark

Answer to Problem 54HP

  f(x)=12|x6|

Explanation of Solution

Given:

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 3.8, Problem 54HP

Concept used:

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

The vertex of the function is (h,k) .

The variables h and k tell how far the graph shifts horizontally and vertically.

The graph opens up if a>0 and opens down if a<0 . If 0<a<1 , the graph is compressed, and if a>1 , it is stretched.

The graph of f(x)=|x| is translated h units horizontally and k units vertically to get the graph of f(x)=a|xh|+k .

Calculation:

Let the function be f(x)=a|xh|+k .

From the graph, it can be observed that the vertex of the function is (6,0) , so the graph is translated 6 units horizontally and 0 units vertically down.

So, h=6 and k=0.

To determine the stretch factor, input the known pair of value. From the graph, (2,2) satisfies the given function.

So, substituting the values in the function f(x)=a|xh|+k.

  2=a|26|+02=a|4|2=4aa=12

Hence, the stretch factor a=12 .

The given function is f(x)=12|x6|.

Conclusion:

Therefore, the given function is f(x)=12|x6| .

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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