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Video: Identifying the Domain and the Range of a Linear Function

Tim Burnham

Given that 𝑥 ∈ {6, 7, 8, 9}, identify the domain and range of the function 𝑦 = 𝑥 − 3.5.

01:46

Video Transcript

Given that 𝑥 is a member of the set six, seven, eight, and nine, identify the domain and range of the function 𝑦 equals 𝑥 minus three point five.

Okay then, let’s first just check that we know what we mean when we say domain and range of a function. Well the domain is the set of inputs to the function. Well that’s quite easy to remember, because the word domain actually has the word IN in it. And the range are the outputs of the function.

So straight away, we’re told the domain in the question; 𝑥 is the set six, seven, eight and nine. Now to find the range, we need to see what effect the function has on each of those input values. And the function is 𝑦 is equal to 𝑥 minus three point five. So it’s taking all of the input values and subtracting three point five from each.

So I’ve just created a little table here to help me work that out. So for my first input value six, if I take away three point five from that, I get two point five. So the input value six maps onto the output value two point five. If I subtract three point five from seven, I find that the input value seven maps onto the output value three point five. Taking away three point five from eight gives me four point five. And taking away three point five from nine gives me five point five. So here I have my set of output values. So the range is the set two point five, three point five, four point five, and five point five. And there’s our answer.