So our domain is - actually let me write this all, all real values, are all real all real values. It's defined for everything in between.Īs we, as we see, once again, as we get to 2, we're here.Īs we cross 2, between 2 and 6, we're here, and at 6, from 6 to 11 we're over here. and x has to be less then or equal to 11. To be greater than 0 or if we say 0 is less than x, and you see that part right over there.Īnd x has to be less than or equal to 11. So in order for this to be defined, x has To 6, we fall into this clause right over here, all the way up to and including 11.īut if we get larger than 11, the function is no longer defined. We follow this clause As we approach 6 but right when we get We're in this clause, it's x crosses 2 and it is greater than 2. And when we look at this, we see, okay, if 0 is The values that x can take on, and actually have this function be defined,Īnd actually figure out what f of x is. The set of all inputs for which our function is defined.Īnd over here, an input variable is x, so to think about, it's the set of all I have a piecewise defined function here,Īnd my goal is to figure out its domain and its range. I'm not sure if this is legit, but the range of the whole function is the union of sets (3, 7], (4, 8], (18, 66] or (3, 7] U (4, 8] U (18, 66]Īm I making myself clear? Please correct me if I made any mistakes. Now you can find the other clauses' y values the same way. What is the range of this clause? that would be 3 < y <= 7 or it can be expressed more 'mathy' as y or the range of the clause = (3, 7] (this means all real values from 3 to 7 (3 is not included, 7 included)) But anyway, for example, we had a piecewise function like this :įind the range of each clause separately.įor 2x+3, 0 < x <= 2, since this is a straight line (with a slope), you just need to find the y values for the endpoints. I don't know if you had done this or not by saying "guess and check for the domain". This answer is a year late, I'm also new to this topic, but I'll try to answer.
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