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 43E

To determine

To find: The piecewise formula for the given function.

Expert Solution & Answer

Answer to Problem 43E

The piecewise function for the given graph of function is y={−x+2, 0<x≤2−13x+53, 2<x≤5.

Explanation of Solution

Given information:

The graph of the function is:

Calculus: Graphical, Numerical, Algebraic, Chapter 1.2, Problem 43E

Calculation:

The graph of the function consists of two straight lines through the points (0,2) , (2,0) and (2,1) , (5,0).

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

m=y2−y1x2−x1=0−22−0=−1

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

y−y0=m(x−x0)y−2=−1(x−0)y−2=−xy=−x+2

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

Use the formula for the slope of line that passes through (2,1) and (5,0).

m=y2−y1x2−x1=0−15−2=−13

The equation of the line passing through the points (2,1) and (5,0).

y−y0=m(x−x0)y−1=−13(x−2)y−1=−13x+23y=−13x+53

So, the equation of the second line is y=−13x+53 defined for 2<x≤5.

Therefore, the piecewise function for the given graph of function is y={−x+2, 0<x≤2−13x+53, 2<x≤5.

Chapter 1.2, Problem 42E

Chapter 1.2, Problem 44E

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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