Question Video: Finding the Range of a Linear Function Given That It Maps from a Given Interval to Real Numbers | Nagwa Question Video: Finding the Range of a Linear Function Given That It Maps from a Given Interval to Real Numbers | Nagwa

# Question Video: Finding the Range of a Linear Function Given That It Maps from a Given Interval to Real Numbers Mathematics • Second Year of Secondary School

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If πβΆ [2, 21] β β, where π(π₯) = 3π₯ β 10, find the range of π.

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### 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, weβre 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.

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