Respuesta :
Answer:
The table which shows that a function's range has exactly three elements is:
x y
3 8
4 6
5 12
6 8
Step-by-step explanation:
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)
Answer:
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)
- x represents input value
- f(x) represents output value
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 : https://brainly.com/question/12153490 ( answered by Eudora )
Find range by table : https://brainly.com/question/12195079 ( answered by AlonsoDehner )
Keywords:
Relation, function, range, co-domain, one-to-one, vertical line test.
