Answers: Part 1 (the ovals) Domain = {-6,-1,1,5,7} Range = {-4,-1,2,4} ------------------- Part 2 (the table) Domain = {1,-3,-2} Range = {-2,5,1} ------------------- Part 3 (the graph) Domain = {1, 2, 3, 4, 5, 6} Range = {-1, 0, 1, 2, 3, 6}
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Explanation:
Part 1 (the ovals) The domain is the set of input values of a function. The input oval is the one on the left. All we do is list the numbers in the input oval to get this list: {-6,-1,1,5,7} The curly braces tell the reader that we're talking about a set of values. So this is the domain.
The range is the same way but with the output oval on the right side List those values in the right oval and we have {-4,-1,2,4} Which is the range. That's all there is to it.
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Part 2 (The tables)
Like with the ovals in part 1, we simply list the input values. The x values are the input values. Notice how this list is on the left side to indicate inputs. So that's why the domain is {1, -3, -2}. Optionally you can sort from smallest to largest if you want. Doing so leads to {-3, -2, 1}
The range is {-2,5,1} for similar reasons. Simply look at the y column
Side Note: we haven't had to do it so far, but if we get duplicate values then we must toss them. ------------------------------ Part 3 (the graph)
Using a pencil, draw vertical lines that lead from each point to the x axis. You'll notice that you touch the x axis at the following numbers: 1, 2, 3, 4, 5, 6 So the domain is the list of those x values (similar to part 2) and it is {1, 2, 3, 4, 5, 6}
Erase your pencil marks from earlier. Draw horizontal lines from each point to the y axis. The horizontal lines will arrive at these y values: -1, 0, 1, 2, 3, 6 So that's why the range is {-1, 0, 1, 2, 3, 6}
Here in this question for finding the numbers that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively we have to first subtract the remainder of the following. By this step we find the highest common factor of the numbers.
And then the required number is the HCF of the following numbers that are formed when the remainder are subtracted from them.
Clearly, the required number is the HCF of the numbers 398−7=391,436−11=425, and, 542−15=527
We will find the HCF of 391, 425 and 527 by prime factorization method.
391=17×23425=52×17527=17×31
Hence, HCF of 391, 4250 and 527 is 17 because the greatest common factor from all the numbers is 17 only.
So we can say that the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.
Note: - whenever we face such a type of question the key concept for solving this question is whenever in the question it is asking about the largest number it divides. You should always think about the highest common factor i.e. HCF. we have to subtract remainder because you have to find a factor that means it should be perfectly divisible so to make divisible we subtract remainder. because remainder is the extra number so on subtracting remainder it becomes divisible.
So, he runs 1.5 then adds 0.5 every day, 1.5 (1.5+0.5)+1.5=x (2.0+0.5)+x=z 2.5+0.5+z=y etc. Why, they want to know the total distance he runs, so thats why you add x,y,z to the end, and you add 2.0+0.5 because he adds 0.5 every dat Plus the other day's miles jogged
