Explanation Given: The function f ( x ) has domain [ 4 , 8 ] and range [ 2 , 6 ] . a. The function is y = f ( x ) + 3 . b. The function is y = f ( x + 3 ) . c. The function is y = f ( 3 x ) . d. The function is y = 3 f ( x ) . Formula used: Domain: In the graph, domain consists of all input values shown on the x − axis. Range: In the graph, co-domain consists of all output values shown on the y − axis. Calculation: Part a: The function is y = f ( x ) + 3 . The domain of y = f ( x ) is [ 4 , 8 ] . We have to find the domain of y = f ( x ) + 3 . The domain of y = f ( x ) + 3 will be same. Now, find the range of y = f ( x ) + 3 . Range will be shift 3 units upwards. [ 2 , 6 ] = [ 2 + 3 , 6 + 3 ] = [ 5 , 9 ] Hence, the domain of y = f ( x ) + 3 is [ 4 , 8 ] and range of y = f ( x ) + 3 is [ 5 , 9 ] . Part b: The function is y = f ( x + 3 ) . The domain of y = f ( x ) is [ 4 , 8 ] . We have to find the domain of y = f ( x + 3 ) . [ 4 , 8 ] = [ 4 + 3 , 8 + 3 ] = [ 7 , 11 ] The domain of y = f ( x + 3 ) is [ 7 , 11 ] . Now, find the range of y = f ( x + 3 )

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 1.1, Problem 77E

To determine

a. Find the domain and range of the function.

b. Find the domain and range of the function.

c. Find the domain and range of the function.

d. Find the domain and range of the function.

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Chapter 1.1, Problem 76E

Chapter 1.1, Problem 78E

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The graph of f(x) is given in the figure below. draw tangent lines to the graph at x=-3,x=-2,x=1,and x=4. estimate f'(-3),f'(-2),f'(1),and f'(4). Round your answers to one decimal place.

Chapter 1 Solutions

CALCULUS (CLOTH)

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a. Find the domain and range of the function. b. Find the domain and range of the function. c. Find the domain and range of the function. d. Find the domain and range of the function.

Solution Summary: The author determines the domain and range of the function f(x).