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Question 1159375: Find the range of the function g:x -> x^2 with the domain {-3,-2,-1,0,1,2}.
Illustrate g by means of a graph.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
The notation g:x -> x^2 is another way of writing g(x) = x^2. The input is x and the rule is to square the input to get the output.
Because g(x) is the output, and so is y, we can say y = g(x)
Therefore, y = x^2 is the same as g(x) = x^2
The domain is the set of allowed input values.
If we plug in x = -3, then we get
y = x^2
y = (-3)^2
y = 9
The input x = -3 leads to the output y = 9
The input x = -2 leads to the output y = 4 since...
y = x^2
y = (-2)^2
y = (-2)*(-2)
y = 4
And so on. You do this for every value in the domain to get this table of values
The range is the set of possible y outputs, given the specific domain. In this case, the range is {0, 1, 4, 9}.
We see that there's some symmetry going on as this graph shows below
I have not connected the points with a parabolic curve because the domain is very specific: we can only allow the values -3, -2, -1, 0, 1, 2
In other words, something like x = 1.5 is not allowed in the domain which is why the portion between x = 1 and x = 2 is not connected with a piece of a curve. The same applies to any other x value not in the domain. This is why we leave the graph as a series of discrete points.
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