![]() ![]() There are infinitely many different numbers that are valid temperatures in degrees Celsius, because it’s a continuous thing. Now this is where it can get a little bit complicated. And that set of output values is called the range. So each one input value relates to a corresponding output value. It’s easy to remember that word because domain contains the word in, and it’s input. If we think of all the possible numbers that we could choose from to input, that set of numbers is called the domain. ![]() Whenever we feed in a number, some magic happens in here and outputs one related number, not two or three to choose from, but one, the answer, the output. It does the processing and spits out the related temperature from the Fahrenheit scale. If we feed in a temperature from the Celsius scale, it does a bit of jigging and warring. Imagine we make a special machine and we feed numbers into that machine, and it carries out some mathematical processing. A relationship where every input is related to exactly one output. And the fact that we’ve got this special relation going on here, so for every input value that you put in, there is only one possible output value, you know what the answer is gonna be, that means we can call this relation a function. For every Celsius temperature, there is exactly one Fahrenheit temperature. So this relation, or relationship, between Celsius temperatures and their corresponding Fahrenheit temperatures is quite a special one, because it’s a one-to-one mapping. So for example, twenty degrees Celsius corresponds to sixty-eight degrees Fahrenheit, so that makes an ordered pair. And when I put an input with its corresponding output, they become an ordered pair. I’ve taken six temperatures and I’ve got the input values, and their corresponding output values. So here is an example of a relation between Celsius temperatures and their Fahrenheit equivalents. So we call this a one-to-one relation, or relationship. There aren’t any temperatures which have one value in Celsius but two or more different possible values in Fahrenheit. But actually, each temperature in Celsius relates to exactly one Fahrenheit equivalent. So zero and thirty-two are an ordered pair and a hundred and two hundred and twelve are an ordered pair. ![]() And we call a Celsius temperature and it’s corresponding Fahrenheit temperature, an ordered pair. ![]() Each Celsius temperature relates to a specific Fahrenheit temperature. So from Celsius to Fahrenheit, and from Fahrenheit to Celsius. In fact, there’s a relation in the other direction as well. Now there is a relationship between the Celsius temperature and it’s corresponding Fahrenheit temperature. The boiling point of water is a hundred degrees on the Celsius scale, or two hundred and twelve degrees on the Fahrenheit scale. For example, the freezing point of water is zero degrees on the Celsius scale, but exactly the same temperature is called thirty-two degrees on the Fahrenheit scale. That gives us two different sets of numbers to represent each individual temperature. Some people use the Fahrenheit scale to quantify their temperatures, and others use Celsius or centigrade. Let’s start by thinking of a situation where we might use a function, temperature say. And this video is designed as a first look, giving you an overview of all these different ideas, and what they might mean, and how they might be used. We’re gonna look at an example of a situation where we’re gonna use a function. And it’s really important to learn and understand this topic. Functions are used in lots of different strands of maths and science. The domain is the set of all the input values of a function and the range is the possible output given by the function.In this video, we’re gonna learn about the terms function, domain, range, and tables of values, or function table. The domain and range of a function are the components of a function. A step-by-step guide to finding domain and range Domain and range of a function The domain and range of any function can be found algebraically or graphically. + Ratio, Proportion & Percentages Puzzles. ![]()
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