Question

What is the range of y = x^2-5 when the domain is {-1, 0, 3, 5}

Answer 1

x = -1
y = (-1)² - 5 = -4

x = 0
y = (0)² - 5 = -5

x = 3
y = (3)² - 5 = 4

x = 5
y = (5)² - 5 = 20

So if the domain is {-1, 0, 3, 5} then range would be {-4, -5, 4, 20}.

Hope this helps.

Answer 2

Comment
Don't get caught believing that all you need check is the 2 endpoints in the domain (-1 and 5) The 5 will give one of the end points of the range, but -1 will not.

f(1) = 1^2 - 5 = 1 - 5 = - 4
However consider this
f(0) = 0^2 - 4 = - 5

So the range for a domain of {-1,0,3,5} is
- 5 ≤ y ≤ 20 for this particular domain.