Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 1.2, Problem 45E

To determine

To find: The piecewise formula for the given function.

Expert Solution & Answer

Answer to Problem 45E

The piecewise function for the given graph of function is y={−x, −1≤x<01, 0<x≤1−12x+32, 1<x<3.

Explanation of Solution

Given information:

The graph of the function is:

Calculus: Graphical, Numerical, Algebraic, Chapter 1.2, Problem 45E

Calculation:

The graph of the function consists of three straight lines passing through the points (−1,1) , (0,0) , (0,1) , (1,1) and (1,1) , (3,0) respectively.

Use the formula for the slope of line that passes through (−1,1) and (0,0).

m=y2−y1x2−x1=0−10−(−1)=−11=−1

The equation of the line passing through the points (−1,1) and (0,0).

y−y0=m(x−x0)y−1=−1(x−(−1))y−1=−1(x+1)y=−x

So, the equation of the first line is y=−x−1 defined for −1≤x<0.

Use the formula for the slope of line that passes through (0,1) and (1,1).

m=y2−y1x2−x1=1−11−0=0

The equation of the line passing through the points (0,1) and (1,1).

y−y0=m(x−x0)y−1=0(x−1)y−1=0y=1

So, the equation of the second line is y=1 defined for 0<x≤1 .

Use the formula for the slope of line that passes through (1,1) and (3,0).

m=y2−y1x2−x1=0−13−1=−12

The equation of the line passing through the points (1,1) and (3,0).

y−y0=m(x−x0)y−1=−12(x−1)y−1=−12x+12y=−12x+32

So, the equation of the third line is y=−12x+32 defined for 1<x<3.

Therefore, the piecewise function for the given graph of function is y={−x, −1≤x<01, 0<x≤1−12x+32, 1<x<3.

Chapter 1.2, Problem 44E

Chapter 1.2, Problem 46E

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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