What are domain and range?
Watch this to understand the domain or range of a function for Higher Maths (get charged up and go)
I recently bought an electric car –because, we should all do what we can to help save the planet and I think it’s important to embrace new technology By the year 2030 EVs or Electric Vehicles will account for 28% of all sales and 58% in 2040, so we know which direction things are going.
When I was considering what car to buy. I had to consider a number of factors like the cost, how long it took to charge the battery and the range – the distance I could travel with a full battery. It turns out that a lot of the things I had to think through when buying my new car share a lot of basic principles with the concepts of Domain and Range we find in Higher Maths.
Domain and Range allows us to understand outputs for a given set of inputs, when we apply a particular function. Also… X and X and X
When I am charging the battery of my car the electricity I am adding is the input going into my car. The input is like the x-values that we enter into the function and we call this the domain.
How far my car can travel is the range of the function, and we use the same word in mathematical language. The range is the y-values that come out of a function.
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Questions in the exam could ask us to state the domain or range of a function.
The following examples show the domain and range of different functions. Remember just like the electricity going into my car the domain is the possible x-values of the function and the range is how far I can drive, the y values coming out.
In this first example y equals log to the base 10 of x, the range is all real values of y, the domain is restricted and takes the values greater than zero. You can see this on the graph.
In the next example we see the graph of y equal x squared. In this one the domain is all real values of x, but the range is restricted and takes all values greater than or equal to zero.
In this one we see the graph of y equals sin x. The domain is all real values of x and the range is between 1 and minus 1.
In this last one we see the graph of y equals one over x. The domain is all real values of x excluding x equals zero. The range is all real values of y, excluding y equals zero. Y equals one over x is an example of a function which is a self-inverse. When we find the inverse of a function the domain and range are switched when the graph is reflected in the line y equals x. In y equals one over x this doesn’t change the function, so the function and its inverse are the same.
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The final concept we need to think about is restrictions on the domain. In school and in our country there are rules and laws we have to follow. There are things we cannot do. The same applies in maths. We can’t divide by zero and we can’t square root a negative number. So when you are asked to find the domain of a function you must look to see if these two laws will be broken for certain values of x. They cannot be in the domain if they will break the law.
In this example we have y equals one over the square root of 2x minus one. First of all we cannot divide by zero so x cannot equal one-half. Also we cannot square root a negative number so 2x minus one must be greater than zero. If we solve that we find that x must be greater than one-half. This is the restricted domain of the function.
You need to make sure you describe the domain and range of functions as fully as possible. Don’t leave in any values that cannot be in the domain, but also make sure you include the ones that should be there.
When I had a petrol car I once made the mistake of putting in diesel fuel instead of unleaded.; a costly mistake. Now all I have to worry about is having enough charge to get me to my destination. For this, I need to understand Domain and Range…