What is the range of the function g(x) = 6 - 2x + x2 given the domain D = {-1, 0, 1, 2}?

Question

 What is the range of the function g(x) = 6 - 2x + x2 given the domain D = {-1, 0, 1, 2}?

Answer 1

Remember that the domain of a function defines all of the possible x values of the function.
Similarly, the range of a function defines all of the possible y values of the function.
Each x-value input gives a y-value output.

To find the range of this function over the given domain, you would need to find out what y-value outputs you get for each x-value input. To do this, you would input each x-value given by your domain into the function.
It will look something like this:
g(-1) = 6 - 2(-1) + x^2 (I'm assuming that the x2 is x^2)
and you would repeat for g(0), g(1), g(2)

The list of y-value outputs is the range of your function :)

Answer 2

 

g(-1) = 6 - 2(-1) + (-1)^2

        = 6 + 2 + 1

        = 9

 

 

g(0) = 6

 

 

g(1) = 6 - 2(1) + 1^2 

       = 6 - 2 + 1

       = 4 + 1

       = 5

 

g(2) = 6 - 2(2) + 2^2

       = 6 - 4 + 4

        = 6

 

The range is {5,6,9}