To find: The domain and range of the function y=−|x|

Expert Solution & Answer

Answer to Problem 41E

Domain=(−∞,∞)Range=(−∞,0]

Explanation of Solution

Given information: Given function is y=−|x|

Concept used:

Domain: - The domain of the function is the set of input for which the given function real and defined.

Range: - The set of value of the dependent variable for which a function is defined.

Since, the range of an absolute function of the form c|ax+b|+k is f(x)≥k

Calculation:

First find the domain of the function y=−|x|

Definition: - The domain of the function is the set of input for which the given function real and defined.

Since the function y=−|x| has neither undefined point nor domain constraints therefore domain is −∞<x<∞ .

In interval notation domain is (−∞,∞)

Now find the range of the function y=−|x|

Definition: - The set of value of the dependent variable for which a function is defined.

Since, the range of an absolute function of the form f(x)=−c|ax+b|+k is f(x)≤k

Here, k=0

Hence, range is −∞<f(x)≤0

In interval notation range is (−∞,0] .

Chapter 3.1, Problem 40E

Chapter 3.1, Problem 42E

Chapter 3 Solutions

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - 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