Question

What is the range of the given function? {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}

Answer 1

The range of given function is {-9, -3, 0, 5, 7}.

Further explanation

A function f is a rule that assigns to each element x in set A exactly one element y or f(x) in set B. Set A is called the domain and set B is called the range of the function f.

Given that a and b are any two any elements, (a, b) is called an ordered pair where a is the first component and b is the second component.

• The relation is a set of ordered pairs.
• The domain is the set of all the first components of the ordered pairs.
• The range is the set of all the second components of the ordered pairs.

{(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)} is a relation since it is a set of ordered pairs.

• Its domain is {-5, -4, -2, 0, 2}
• Its range is {-9, -3, 0, 5, 7}

The relation above is represented by a list. This relationship can also be represented by the following:

• a table
• a map
• a graph

See the attachment for details.

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Keywords: what is, the range of the given function, {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}, domain, set, elements, ordered pairs, first components, second, represented by a list, a table, a map, a graph

Answer 2

The range of the function $\{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\}$ is $\fbox{\begin\\\ \{0,-3,-9,5,7\}\\\end{minispace}}$.

Further explanation:

A function is defined as a relation between the independent variable and the dependent variable.

In a function of the form $y=f(x)$ the independent variable is represented by $x$ and the dependent variable is represented by $y$.

The ordered pair of the form $(x,y)$ represent the order in which the dependent variable and the independent variable is placed.

For example: Consider a function as $\{(a,b),(c,d),(e,f),(g,h)\}$ in which first element of each ordered pair is an element of domain set and the second element of each ordered pair is an element of range set.

The function is also defined as a rule under which each element of domain set is mapped to the range set such that each element of range set has a unique pre-image in the domain set.

Figure 1 (attached in the end) represents the mapping of each element of domain set to range set.

The set of all the values of $x$ is called the domain of the function and the set of all the value of $y$ is called the range of the function.

The set of ordered pair for a function is given as $\{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\}$.

The first element of the each ordered pair is the element of the domain set for the function.

The second element of each ordered pair is the element of the range set for the function.

The domain set is represented as $\{-2,-4,2,0,-5\}$ and the range set is represented as $\{0,-3,-9,5,7\}$.

Figure 2 (attached in the end) represents the mapping of each element of domain set of the given function to range set of the given function.

Therefore, the range of the function $\{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\}$ is $\fbox{\begin\\\ \{0,-3,-9,5,7\}\\\end{minispace}}$

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Answer details  

Grade: High school  

Subject: Mathematics

Chapter: Relation and Function

Keywords: Relation, function, domain set, range set, domain, range, variable, dependent variable, independent variable, ordered pair, cartesian product,{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7).