Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…

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Question

Chapter 5.6, Problem 72E

To determine

Tograph: the function and its inverse function and explain why it is its own inverse.

Expert Solution

Explanation of Solution

Given information:

the function is f(x)=−x .

Graph: to graph the function, use plotting point method,

x	f(x)
2	−2
1	−1
3	−3

Now, using above table plot points and joint them smoothly,

The graph can be observed as:

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 5.6, Problem 72E , additional homework tip 1

Interpretation: from theabove graph it can be observed that the function graph and inverse function graph are same because function and inverse functions are reflection in the line y=x and after reflecting the graph in the line y=x , it gives same.

To find the inverse function substitute f(x)=y in the function and simplify,

f(x)=−xy=−x [substitute f(x)=y]x=−yf−1(x)=−x [simplify]f−1(x)=f(x)

To determine

To graph: the other linear functions that are their own inverses.

Expert Solution

Explanation of Solution

Given information:

the functions are their own inverses.

Graph: let function f(x)=x ,

to graph the function, use plotting point method,

x	f(x)
2	2
1	1
3	3

let function f(x)=1x ,

to graph the function, use plotting point method,

x	f(x)
2	12
1	1
3	13

Now, using above table plot points and joint them smoothly,

The graphs can be observed as:

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 5.6, Problem 72E , additional homework tip 2

Interpretation: from theabove graph it can be observed that the function graph are their own inverses.

To determine

To calculate : the general equation that describe the family of linear functions that are their own function.

Expert Solution

Answer to Problem 72E

The general equation is f(x)=xn,n∈{1,−1} .

Explanation of Solution

Given information : the functions are their own inverses.

Calculation : from the part (b), it can be observed that the general equation for functions that are their own inverses can be written as:

f(x)=xn,n∈{1,−1}

Chapter 5.6, Problem 71E

Chapter 5.6, Problem 73E

Chapter 5 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - 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