BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.1, Problem 51E
To determine

To find: An expression for the function that represents the given graph.

Expert Solution

Answer to Problem 51E

The expression for the function that represents the given graph is f(x)={x+3 if 0x32x6if 3<x5.

Explanation of Solution

Formula used:

Slope intercept form, y=mx+c.

Point slope form, yy1=m(xx1).

Calculation:

From the given graph, it is clear that there exist two lines with different domains. So, it leads to a piecewise function.

Notice that, the graph contains two straight lines.

One line has slope −1 and y-intercept is 3 on the domain 0x3 and the other line has slope 2 and passes through (3,0) on the domain 3<x5.

Use slope intercept form and obtain the equation of the line with slope −1 and y-intercept 3.

y=(1)x+3

y=x+3 (1)

Use point slope form and obtain the equation of the line with slope 2 and the point (3,0).

y0=2(x3)

y=2x6 (2)

Combine equations (1) and (2) and the domains to obtain the required function.

That is, the piecewise function of the given graph is f(x)={x+3 if 0x32x6if 3<x5.

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