Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Question

Chapter 1.2, Problem 41E

To determine

To find: The piecewise formula for the given function.

Expert Solution & Answer

Answer to Problem 41E

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

Explanation of Solution

Given information: The graph of the function is:

Calculus: Graphical, Numerical, Algebraic, Chapter 1.2, Problem 41E

Calculation:

The graph of the function consists of two straight lines that passes through the points (0,0) , (1,1) and (1,1) , (2,0) respectively.

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

m=y2−y1x2−x1=1−01−0=1

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

y−y0=m(x−x0)y−0=1(x−0)y=x

So, the equation of the first line is y=x.

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

m=y2−y1x2−x1=0−12−1=−1

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

y−y0=m(x−x0)y−1=−1(x−1)y−1=−x+1y=−x+2

So, the equation of the second line is y=−x+2.

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

Chapter 1.2, Problem 40E

Chapter 1.2, Problem 42E

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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