Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Differential Equations

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Question

Chapter 1.2, Problem 46E

To determine

To find: The piecewise formula for the given function.

Expert Solution & Answer

Answer to Problem 46E

The piecewise function for the given graph of function is y={12x, −2≤x≤0−2x+2, 0<x≤1−1, 1<x≤3.

Explanation of Solution

Given information:

The graph of the function is:

Calculus: Graphical, Numerical, Algebraic, Chapter 1.2, Problem 46E

Calculation:

The graph of the function consists of three straight lines passing through the points (−2,−1) , (0,0) , (0,2) , (1,0) and (1,−1) , (3,−1) respectively.

Use the formula for the slope of line that passes through (−2,−1) and (0,0).

m=y2−y1x2−x1=0−(−1)0−(−2)=12

The equation of the line passing through the points (−2,−1) and (0,0).

y−y0=m(x−x0)y−(−1)=12(x−(−2))y+1=12(x+2)y=12x

So, the equation of the first line is y=12x defined for −2≤x≤0.

Use the formula for the slope of line that passes through (0,2) and (1,0).

m=y2−y1x2−x1=0−21−0=−21=−2

The equation of the line passing through the points (0,2) and (1,0).

y−y0=m(x−x0)y−2=−2(x−0)y−2=−2xy=−2x+2

So, the equation of the second line is y=−2x+2 defined for 0<x≤1 .

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

m=y2−y1x2−x1=−1−(−1)3−1=0

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

y−y0=m(x−x0)y−(−1)=0(x−1)y+1=0y=−1

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={12x, −2≤x≤0−2x+2, 0<x≤1−1, 1<x≤3.

Chapter 1.2, Problem 45E

Chapter 1.2, Problem 47E

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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