Domain, Range, independent and dependent variables

Instructions: To get the domain of a graph you have to look at the line. If it is a line that keeps going forever you look at where it hits the x, once you see that you can put [whatever the x is, oo) (-oo, whatever the x is]. Now if the line stops at a certain point, you get the x of the two tips of the line and you put the higher point first such as [65,-43] Now these numbers are also the independent variables.

To get the range of a graph it is a lot like doing the domain but with the y instead of x. All you really have to do is see where the y starts and stops, it could be infinitive or it could stop, but that is what you look at. When you find that out you have also found the dependent variable.


Examples:
105A





In this problem you can see that there is no line so all you have to find is the x and the y of the points and put them in chronological order and then you are done. So for the domain, 0, 1, 2, and since it goes from 0 - 2 you can write the domain like this (0,2) and this is also the independent variables. The range in this graph would be [1, -2] because the y goes from 1 to -2, which then is also the dependent variable.

105B



Domain / independent variable- [-1, 1]
Range / Dependent Variable- [-1, 2]

105C






Some people may think that this looks confusing but it really isn’t, because the two lines are on the same x value when the opened circle ends and the closed begins mean that you can just combine the two make the independent variable and the domain are [-2, 2]. The range/ dependent variables does the same thing so it would be [2,-2].



105D




In this problem you just look at where the farthest x is to the left and you have your first number, which is -2. The second number in the domain would be 1 because that’s the farthest to the right the x goes. So the final domain would be [-2,1]. The range would be [2, -2] because the highest point and the lowest point which all connects is 2 and -2 which makes it the range.0