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Chapter 2: Q. 42 (page 101)

In Problems 41鈥�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)=10<x鈮�2x-1鈮�x鈮�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

It can be seen from the graph that,

f(x)=1,0<x鈮�2

The part of graph below the x-axis represents a line that passes through (0,0).

Also for 0鈮�x鈮�1, the function will be,

f(x)=x

03

Step 3. Defining the function 

So, the function will be,

f(x)=10<x鈮�2x-1鈮�x鈮�0

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Most popular questions from this chapter

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Exploration Graph y=x3. Then on the same screen graph y=(x-1)3+2. Could you have predicted the result?

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Consider the equation

y=1ifxisrational0ifxisirrational

Is this a function? What is its domain? What is its range? What is its y-intercept, if any? What are its x-intercepts, if any? Is it even, odd, or neither? How would you describe its graph?
See all solutions

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