Video Transcript
𝑋 and 𝑌 are two sets of numbers
where set 𝑋 contains the values 10, one, two, and eight and set 𝑌 contains the
values 12, seven, 60, six, 48, and four. The function 𝑓 of 𝑥 is equal to
six 𝑥, where 𝑓 maps elements of 𝑋 onto elements of 𝑌. Find the ordered pairs that satisfy
the function and its range.
One way of answering this question
is to consider a mapping diagram that represents the function 𝑓. There are four elements in set
𝑋. They are the numbers 10, one, two,
and eight. Set 𝑌 contains six elements, the
values 12, seven, 60, six, 48, and four. We are told that the function 𝑓 of
𝑥 is equal to six 𝑥. We recall that the domain of 𝑓 is
the set of inputs for which 𝑓 of 𝑥 is defined. And the range of 𝑥 is the set of
corresponding outputs.
Our first value in set 𝑋 is
10. And since 𝑓 of 𝑥 is equal to six
𝑥, 𝑓 of 10 is equal to six multiplied by 10. This is equal to 60 and means that
an input of 10 gives an output of 60. The first ordered pair that
satisfies the function is 10, 60. 𝑓 of one is equal to six
multiplied by one, which equals six. This gives us a second ordered pair
one, six. Repeating this for the third value
in set 𝑋, we have 𝑓 of two is equal to 12, giving us a third ordered pair two,
12. Finally, 𝑓 of eight is equal to
48. And we have a fourth ordered pair
eight, 48. The four ordered pairs that satisfy
the function are 10, 60; one, six; two, 12; and eight, 48.
We are also asked to give the range
of the function. As already mentioned, this is the
set of all outputs of 𝑓 of 𝑥. The range of the function is
therefore the set of the four values 60, six, 12, and 48. And we have now answered the two
parts of this question.
