(a) Answer The dependent variable is s and independent variable is t . Explanation Given: Weekly sales s fluctuate by the function s ( t ) = − 2 | t − 20 | + 40 where t is the time in weeks. The dependent variables are those variables that depends on another variable and changes accordingly. It provides output values for the function. On the other hand, the independent variable is free from the dependency on the another variable and it is the input variable of the function. In the given problem it can be observed that the weekly sales increases and decreases with time. The weekly sales totally depend on the time and time is free from any dependency. Therefore, the dependent variable is weekly sales s and the independent variable is t as per the definition of dependent and independent variables. (b) To determine To graph: The function s = − 2 | t − 20 | + 40 with the transformation from the graph f ( x ) = | x | . Answer Explanation Given: The base function is f ( x ) = | x | . Concept used: The function y = f ( x ) + c moves up by c unit when c > 0 and moves down by c unit when c < 0 with base function f ( x ) . The function y = f ( x + c ) moves left by c unit when c > 0 and moves right by c unit when c < 0 with base function f ( x ) . The function y = c f ( x ) stretches in the y direction when c > 1 and compresses when 0 < c < 1 with base function f ( x ) . The function reflect itself about x if the function is y = − f ( x ) . Graph: The base function is f ( x ) = | x | . Draw the graph of f ( x ) = | x | as shown in Figure 1. Now to draw the graph of the equation s = − 2 | t − 20 | + 40 use the transformation. Use the concepts of transformations. First shift the graph rightward by 20 units since the value of c is negative. Second reflect the graph since the value of y = − f ( x ) . Third stretch the graph in the y direction since the value is 2. Fourth move the graph by 40 units since the value of 40 is greater than 0. Interpretation: It can be seen that the graph passes through the origin.

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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Question

Chapter 3, Problem 14CT

(a)

To determine

To identify: The variables which is independent and dependent.

(a)

Expert Solution

Answer to Problem 14CT

The dependent variable is s and independent variable is t .

Explanation of Solution

Given:

Weekly sales s fluctuate by the function s(t)=−2|t−20|+40 where t is the time in weeks.

The dependent variables are those variables that depends on another variable and changes accordingly. It provides output values for the function.

On the other hand, the independent variable is free from the dependency on the another variable and it is the input variable of the function.

In the given problem it can be observed that the weekly sales increases and decreases with time.

The weekly sales totally depend on the time and time is free from any dependency.

Therefore, the dependent variable is weekly sales s and the independent variable is t as per the definition of dependent and independent variables.

(b)

To determine

To graph: The function s=−2|t−20|+40 with the transformation from the graph f(x)=|x| .

(b)

Expert Solution

Answer to Problem 14CT

Explanation of Solution

Given:

The base function is f(x)=|x| .

Concept used:

The function y=f(x)+c moves up by c unit when c>0 and moves down by c unit when c<0 with base function f(x) .

The function y=f(x+c) moves left by c unit when c>0 and moves right by c unit when c<0 with base function f(x) .

The function y=cf(x) stretches in the y direction when c>1 and compresses when 0<c<1 with base function f(x) .

The function reflect itself about x if the function is y=−f(x) .

Graph:

The base function is f(x)=|x| .

Draw the graph of f(x)=|x| as shown in Figure 1.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015, Chapter 3, Problem 14CT , additional homework tip 1

Now to draw the graph of the equation s=−2|t−20|+40 use the transformation.

Use the concepts of transformations.

First shift the graph rightward by 20 units since the value of c is negative.

Second reflect the graph since the value of y=−f(x) .

Third stretch the graph in the y direction since the value is 2.

Fourth move the graph by 40 units since the value of 40 is greater than 0.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015, Chapter 3, Problem 14CT , additional homework tip 2

Interpretation:

It can be seen that the graph passes through the origin.

Chapter 3, Problem 13CT

Chapter 3, Problem 1CA

Chapter 3 Solutions

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

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