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Chapter 2: Q. 44 (page 101)

In Problems 41–44, the graph of a piecewise-defined function is given. Write a definition for each function.

Short Answer

Expert verified

The piecewise-defined function is,

f(x)=2x+2-1≤x≤0xx>0

Step by step solution

01

Step 1. Given Information 

We are given a graph of a piecewise-defined function,

02

Step 2. Defining the function  

For the point 0,2means when x=0,

f(2)=2 that means the y-intercept is2.

It can be seen from the graph that for the points with the x-coordinates is between -1 and 0, both inclusive, the value of the y- coordinate is twice the value of the x-coordinate.

So, for -1≤x≤0the function will be,

f(x)=2x+2

03

Step 3. Defining the function

Similarly, the point (1,1)means when x=1

f(1)=1and

when x=2,

f(2)=2

The line passes to origin so there is no y-intercept.

So, it can be seen from the graph that for x>0, the function will be,

f(x)=0

So, the piecewise-defined function will be,

f(x)=2x+2-1≤x≤0xx>0

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