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