# What shifting and shrinking operations must be operated on the function y = t 2 to obtain the function y = f ( t ) ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.5, Problem 89E

a.

To determine

## What shifting and shrinking operations must be operated on the function y=t2 to obtain the function y=f(t)

Expert Solution

To shift upward 4 units, shrink vertically by a factor of 0.01

### Explanation of Solution

Given information : The question is

The annual sales of a certain company can be modeled by the function f(t)=4+0.01t2 , where t represents years since 1990

Calculation : The particular equation is

f(t)=4+0.01t2

To obtain y=f(t) from y=t2 , its shift by 4 units upward and shrink by 100 times

b.

To determine

### To transform the new function y=g(t)

Expert Solution

The shift to the right 10 units, g(t)=4+0.01(t10)2

### Explanation of Solution

Given information : The question is

Calculation : To represent year since 2000 instead of 1990 , there will be a horizontal shift by 10 units

That means,

The new function will be g(t)=4+0.01(t10)2

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