Explanation Consider the graphs f ( x ) = 2 − 1 2 x and g ( x ) = 2 − x . To draw the region first draw the individual graphs. Consider the function f ( x ) = 2 − 1 2 x , The graph for the function f ( x ) = 2 − 1 2 x is drawn by constructing the table for its values. For x = 0 , substitute 0 for x , f ( x ) = 2 − 1 2 ( 0 ) = 2 For x = − 2 , substitute − 2 for x , f ( x ) = 2 − 1 2 ( − 2 ) = 2 + 1 = 3 For x = 2 , substitute 2 for x , f ( x ) = 2 − 1 2 ( 2 ) = 2 − 1 = 1 Construct the table, using various values of x and y , for the function f ( x ) = 2 − 1 2 x . x 0 − 2 2 f ( x ) 2 3 1 Now, consider the function g ( x ) = 2 − x , The graph for the function g ( x ) = 2 − x is drawn by constructing the table for its values. For x = 0 , substitute 0 for x . g ( x ) = 2 − 0 = 2 For x = 1 , substitute 1 for x , g ( x ) = 2 − 1 = 2 − 1 = 1 For x = 4 , substitute 4 for x , g ( x ) = 2 − 4 = 2 − 2 = 0 Construct the table, using various values of x and y , for the function g ( x ) = 2 − x . x 0 1 4 g ( x ) 2 1 0 For the common region first, compute the intersection point for both the functions f ( x ) = 2 − 1 2 x and g ( x ) = 2 − x . Equate the above equations. 2 − x = 2 − 1 2 x x = 1 2 x Square both the sides, x = ( 1 2 x ) 2 x = x 2 4 x 2 4 − x = 0 Take the x variable common, x ( x 4 − 1 ) = 0 Recall the zero-factor property that is when A B = 0 , then A = 0 or B = 0 , where A and B are algebraic expressions

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ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 7.1, Problem 14E

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The value among the following $(a)1 (b)6 (c)−3 (d)3 (e)4$ that best represents the area of the region bounded by the graphs $f(x)=2−12x$ and $g(x)=2−x$ .

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Chapter 7.1, Problem 13E

Chapter 7.1, Problem 15E

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The value among the following ( a ) 1 ( b ) 6 ( c ) − 3 ( d ) 3 ( e ) 4 that best represents the area of the region bounded by the graphs f ( x ) = 2 − 1 2 x and g ( x ) = 2 − x .

Solution Summary: The author explains that the value that best represents the area of the region bounded by the graphs is option (a)1.

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The value among the following $(a)1 (b)6 (c)−3 (d)3 (e)4$ that best represents the area of the region bounded by the graphs $f(x)=2−12x$ and $g(x)=2−x$ .

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