BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

1st Edition

ISBN: 9781608408382

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Question

Chapter 3.1, Problem 43E

To determine

To find : The domain and range of the function y=4−|x|

Expert Solution & Answer

Answer to Problem 43E

Domain=(−∞,∞)Range=(−∞,4]

Explanation of Solution

Given information : Given function is y=4−|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

First find the domain of the function y=4−|x|

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

Since the function y=4−|x| has no undefined point nor domain constraints therefore domain is −∞<x<∞ .

In interval notation domain is (−∞,∞)

Now find the range of the function y=4−|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

Write the function y=4−|x| of the form f(x)=−c|ax+b|+k , which is given below

f(x)=−|x|+4

Here, k=4

Hence, range is −∞<f(x)≤4

In interval notation range is (−∞,4] .

Chapter 3.1, Problem 42E

Chapter 3.1, Problem 44E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 1: Common Core 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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The domain and range of the function y = 4 − | x |

Concept explainers

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To find : The domain and range of the function y=4−|x|

Answer to Problem 43E

Explanation of Solution

Chapter 3 Solutions