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: 9781319434540

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

Chapter 1 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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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).