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Chapter 2: Q. 10 (page 68)

True or False Every relation is a function.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Step 1. Given information 

In the given question we have to explain the given statement is true or false.

The statement is "Every relation is a function."

02

Step 2. Definition of Relation and Function 

Relation-The relation is defined as the collection of ordered pairs, which contains an object from one set to the other set.

Functions-The relation that defines the set of inputs to the set of outputs is called the functions. In function, each input in the set X has exactly one output in the set Y.

03

Step 3. All functions are relations but all relations are not functions.

Hence, the given statement is false.

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Most popular questions from this chapter

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=x2+4

If f(x)=x3if-2≤x<13x+2if1≤x≤4

Find: (a)f(-1) (b)f(0) (c)f(1) (d)f(3)

In Problems 7–18, 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

If fis a function defined by the equation y=f(x), then x is called the ____________ variable and y is the ____________ variable.

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

g(x)=-x3
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