Which table shows a function whose range has exactly three elements

The table which shows that a function's range has exactly three elements is:

         x      y

         3      8

        4      6

        5      12

        6       8

Domain of a function--

The domain of a function is the set of all the x-values i.e. the value of the independent variable for which a function is defined.

Range of a function--

It is the set of all the y-value or the values which are obtained by the independent variable i.e. the values obtained by the function in it's defined domain.

a)

     x      y

     1      4

     2      4

     3       4

Domain: {1,2,3}

Range: {4}

Hence, the range has a single element.

b)

     x      y

     3      8

     4      6

     5      12

     6       8

Domain: {3,4,5,6}

Range: {6,8,12}

Hence, the range has three element.

c)

     x      y

     0     5

     2      9

     0      15

This relation is not a function.

because 0 has two images.

0 is mapped to 5 and 0 is mapped to 15.

d)

     x      y

     1      4

     3     2

    5      1  

    3      4

This relation is not a function.

because 3 has two images.

3 is mapped to 2 in the ordered pair (3,2) and 3 is mapped to 4 in the ordered pair (3,4)

The required table would be,

 x         3     4      5      6

f(x)       8     6     12     8

Option 2 is correct

Explanation:

The table in which there are only 3 different value of f(x) shows the function, whose range has exactly three elements.( three different value)

Further Explanation:

Since, a relation is called a function,  If there is only one output value for each input value.

For any function, f(x)

The set of all possible output values of a function is called  range.

The set of all input value of a function is called domain.

# In table 1,

x        1       2      3

f(x)    4       4      4

f(x) is a function.

Its range = {4}

Thus, range has exactly one element.

# In table 2,

x        3       4      5     6

f(x)    8       6     12    8

f(x) is a function,

Its range = {8, 6, 12}

Thus, range has exactly three elements.

# In table 3,

x        0       2       0

f(x)    5       9      15

There are two outputs, 5 and 15 for the input value 0,

Thus, f(x) is not a function,

# In table 4,

x        1       3       5     3

f(x)    4       2       1      4

There are two outputs, 2 and 4 for the input value 3,

Thus, f(x) is not a function,

Learn More:

Table represents function :  ( answered by Eudora )

Find range by table :  ( answered by AlonsoDehner )

Keywords:

Relation, function, range, co-domain, one-to-one, vertical line test.

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what is the image?