what is the range of the function f(x)=(x-1)^2 when the domain is {-5,0,5}?

Answer 1

The range for any function is the set of all the possible outputs of a function given a specific set input values for a function. In other words, all the possible y-values given specific x-values. In this case because there is no negative sign outside the parenthesis that is being squared all values are going to be positive and because all quadratic functions are symmetrical, all y-values on one side will be the same on the other side at an equal distance from the maximum or minimum. With this in mind, solve for y at 0 and 5 to get a range of 1 to 16.

Answer 2

When the domain is a set of discrete (not continuous) numbers and you want to find the range, all you need to do is plug those numbers in and see what you get for your answers.

In this case, -5 --> 36, 0 --> 1, and 5 --> 16