Video Transcript
If 𝑓 maps elements on the closed
interval from two to 21 to the set of real numbers, where 𝑓 of 𝑥 is equal to three
𝑥 minus 10, find the range of 𝑓.
In this question, we are given a
linear function 𝑓 of 𝑥, which is equal to three 𝑥 minus 10. We know that the graph of 𝑦 is
equal to three 𝑥 minus 10 is a straight line as shown. We know that the domain of a
function is the set of input or 𝑥-values. And in this question, we’re told
that these lie on the closed interval from two to 21. The function 𝑓 of 𝑥 is therefore
defined for all values between the two points shown.
We can calculate the corresponding
𝑓 of 𝑥 values by substituting 𝑥 equals two and 𝑥 equals 21 into the
function. When 𝑥 is equal to two, 𝑓 of 𝑥
is equal to three multiplied by two minus 10. This is equal to negative four. Likewise, when 𝑥 is equal to 21,
𝑓 of 𝑥 is equal to three multiplied by 21 minus 10. This is equal to 53. Since the range of a function 𝑓 is
the set of outputs or 𝑦-values, we can conclude that 𝑓 of 𝑥 or 𝑦 is greater than
or equal to negative four and less than or equal to 53. Using interval notation, the range
of the function 𝑓 on the given domain is the closed interval from negative four to
53.
