Explanation Given: The data points are ( 1 , 2 ) , ( 4 , 9 ) and ( 6 , 3 ) Formula used: m = y 2 − y 1 x 2 − x 1 y − y 1 = m ( x − x 1 ) Calculation: ( a ) To determine the piecewise-linear function, first we find the equation of the line that connecting the points ( 1 , 2 ) and ( 4 , 9 ) . And then for the second function, we find the equation of the line that connects the points ( 4 , 9 ) and ( 6 , 3 ) . So to find the equation of the line connecting ( 1 , 2 ) and ( 4 , 9 ) , first we find the slope using the formula of slope of the line connecting ( x 1 , y 1 ) and ( x 2 , y 2 ) is: m = y 2 − y 1 x 2 − x 1 So the slope is m = 9 − 2 4 − 1 = 7 3 So using point slope form, the equation of the line is y − 2 = 7 3 ( x − 1 ) y − 2 = 7 3 x − 7 3 y = 7 3 x − 7 3 + 2 y = 7 3 x − 1 3 Similarly the slope of the line connecting ( 4 , 9 ) and ( 6 , 3 ) is: m = 3 − 9 6 − 4 = − 6 2 = − 3 And now using the point slope form, the equation of line is y − 9 = − 3 ( x − 4 ) y − 9 = − 3 x + 12 y = − 3 x + 21 Hence the piecewise-linear function in the domain 1 ≤ x ≤ 6 is: f ( x ) = { 7 3 x − 1 3 if 1 ≤ x ≤ 4 − 3 x + 21 if 4 ≤ x ≤ 6 ( b ) Now since x=5 lies in the interval 1 ≤ x ≤ 6 , so we use the second function

College Algebra with Modeling & Visualization (5th Edition)

5th Edition

ISBN: 9780321826138

Author: Gary K. Rockswold

Publisher: PEARSON

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Chapter 2, Problem 68RE

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( a ) The formula for a piecewise-linear function f that passes through the data points whose domain is 1≤x≤6 .

( b ) The value of f( 5 ) .

( c ) If the function f is continuous on its domain.

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Chapter 2, Problem 67RE

Chapter 2, Problem 69RE

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College Algebra with Modeling & Visualization (5th Edition)

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( a ) The formula for a piecewise-linear function f that passes through the data points whose domain is 1 ≤ x ≤ 6 . ( b ) The value of f ( 5 ) . ( c ) If the function f is continuous on its domain.

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( a ) The formula for a piecewise-linear function f that passes through the data points whose domain is 1≤x≤6 . ( b ) The value of f( 5 ) . ( c ) If the function f is continuous on its domain.

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Chapter 2 Solutions

( a ) The formula for a piecewise-linear function f that passes through the data points whose domain is 1≤x≤6 .

( b ) The value of f( 5 ) .

( c ) If the function f is continuous on its domain.