the domain for g(x)=5x-1 is -2 less than or equal to x which is less than or equal to 2.?

Question

what is the smallest value in the range of g(x)

Answer 1

Since this is a "linear" function, the minimum value in the range must be at one endpoint or the other. (That is, there's no chance that the function will "curve" out in the middle.)

So just check the endpoints of the range.

g(-2) = 5(-2) - 1 = -10 - 1 = -11
g(2) = 5(2) - 1 = 10 - 1 = 9

-11 is smaller than 9, so the smallest value in the range is -11.

(PS -- You can ignore this, but I feel I need to post it too. As an extra note, however, the word "smallest" is a little ambiguous. A better word would be "least". Sometimes people consider "small" and "large" to be measurements of magnitude rather than value, so one could say 10 is "smaller" than -11 because 11 is bigger than 10. By that logic, 0 would be the "smallest" number in the range.)