Answer 3 f ( x ) stretches the graph of the function f ( x ) = 3 x + 4 vertically by factor of 3 Explanation Given information: f ( x ) = 3 x + 4 ; h ( x ) = 3 f ( x ) Concept Involved: Rules for Transformation of Function is given below in the table: Transformation Function Description Horizontal Shift f ( x + h ) Shift left h units f ( x − h ) Shift right h units Vertical shift f ( x ) + k Shift upwards k units f ( x ) − k Shift downwards k units Reflection − f ( x ) Reflection over x-axis f ( − x ) Reflection over y-axis Vertical Stretch a f ( x ) , a > 1 Stretch vertically by a factor of a Vertical Compress a f ( x ) , 0 < a < 1 Compress vertically by a factor of a Horizontal Stretch f ( b x ) , b > 1 Compress horizontally by a factor of 1 b Horizontal Compress f ( b x ) , 0 < b < 1 Stretch horizontally by a factor of 1 b Graph: Interpretation: From the above table and the graph we see that 3 f ( x ) stretches the graph of the function f ( x ) = 3 x + 4 vertically by factor of 3

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

1st Edition

ISBN: 9781680331141

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Concept explainers

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 3, Problem 29CR

To determine

To find : the graph of function, transformation and its description

Expert Solution & Answer

Answer to Problem 29CR

3f(x) stretches the graph of the function f(x)=3x+4 vertically by factor of 3

Explanation of Solution

Given information: f(x)=3x+4 ; h(x)=3f(x)

Concept Involved:

Rules for Transformation of Function is given below in the table:

Transformation	Function	Description
Horizontal Shift	f(x+h)	Shift left h units
f(x−h)	Shift right h units
Vertical shift	f(x)+k	Shift upwards k units
f(x)−k	Shift downwards k units
Reflection	−f(x)	Reflection over x-axis
f(−x)	Reflection over y-axis
Vertical Stretch	af(x), a>1	Stretch vertically by a factor of a
Vertical Compress	af(x), 0<a<1	Compress vertically by a factor of a
Horizontal Stretch	f(bx), b>1	Compress horizontally by a factor of 1b
Horizontal Compress	f(bx), 0<b<1	Stretch horizontally by a factor of 1b

Graph:

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015, Chapter 3, Problem 29CR

Interpretation:

From the above table and the graph we see that 3f(x) stretches the graph of the function f(x)=3x+4 vertically by factor of 3

Chapter 3, Problem 28CR

Chapter 3, Problem 30CR

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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