Explanation Given: The function is f ( x ) = x 2 a. y = f ( x + 1 ) b. y = f ( x ) + 1 c. y = f ( 5 x ) d. y = 5 f ( x ) Calculation: Part a: Find the points to draw the graph of the function y = f ( x + 1 ) . The given function is f ( x ) = x 2 . Substitute x + 1 in place of x . f ( x + 1 ) = ( x + 1 ) 2 Put x = − 2 in the given function. f ( x + 1 ) = ( − 2 + 1 ) 2 = ( − 1 ) 2 = 1 Put x = − 1 in the given function. f ( x + 1 ) = ( − 1 + 1 ) 2 = ( 0 ) 2 = 0 Put x = 0 in the given function. f ( x + 1 ) = ( 0 + 1 ) 2 = ( 1 ) 2 = 1 Put x = 1 in the given function. f ( x + 1 ) = ( 1 + 1 ) 2 = ( 2 ) 2 = 4 Put x = 2 in the given function. f ( x + 1 ) = ( 2 + 1 ) 2 = ( 3 ) 2 = 9 The points are: x − 2 − 1 0 1 2 f ( x ) 1 0 1 4 9 The graph is: Part b: Find the points to draw the graph of the function y = f ( x ) + 1 . The given function is f ( x ) = x 2 . We can rewrite it as: f ( x ) + 1 = x 2 + 1 Put x = − 2 in the given function. f ( x ) + 1 = ( − 2 ) 2 + 1 = 4 + 1 = 5 Put x = − 1 in the given function. f ( x ) + 1 = ( − 1 ) 2 + 1 = 1 + 1 = 2 Put x = 0 in the given function. f ( x ) + 1 = ( 0 ) 2 + 1 = 0 + 1 = 1 Put x = 1 in the given function. f ( x ) + 1 = ( 1 ) 2 + 1 = 1 + 1 = 2 Put x = 2 in the given function. f ( x ) + 1 = ( 2 ) 2 + 1 = 4 + 1 = 5 The points are: x − 2 − 1 0 1 2 f ( x ) 5 2 1 2 5 The graph is:

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 1.1, Problem 78E

To determine

a. Draw the graph of the function over [−2,2].

b. Draw the graph of the function over [−2,2].

c. Draw the graph of the function over [−2,2].

d. Draw the graph of the function over [−2,2].

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Chapter 1.1, Problem 77E

Chapter 1.1, Problem 79E

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Chapter 1 Solutions

CALCULUS (CLOTH)

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a. Draw the graph of the function over [ − 2 , 2 ] . b. Draw the graph of the function over [ − 2 , 2 ] . c. Draw the graph of the function over [ − 2 , 2 ] . d. Draw the graph of the function over [ − 2 , 2 ] .

Solution Summary: The author explains how to draw the graph of the function y=f(x+1).

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a. Draw the graph of the function over [−2,2].

b. Draw the graph of the function over [−2,2].

c. Draw the graph of the function over [−2,2].

d. Draw the graph of the function over [−2,2].

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Chapter 1 Solutions

a. Draw the graph of the function over [ − 2 , 2 ] . b. Draw the graph of the function over [ − 2 , 2 ] . c. Draw the graph of the function over [ − 2 , 2 ] . d. Draw the graph of the function over [ − 2 , 2 ] .

Solution Summary: The author explains how to draw the graph of the function y=f(x+1).

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a. Draw the graph of the function over [−2,2]. b. Draw the graph of the function over [−2,2]. c. Draw the graph of the function over [−2,2]. d. Draw the graph of the function over [−2,2].

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Chapter 1 Solutions

a. Draw the graph of the function over [−2,2].

b. Draw the graph of the function over [−2,2].

c. Draw the graph of the function over [−2,2].

d. Draw the graph of the function over [−2,2].