range of f(x) = (x^2) + 3 after restricting domain

[lyzhou1990]

I came across this practice problem in an old SAT II Math prep book, which I don't understand. Here it is:

If we restrict the domain of the f(x) = (x^2) + 3 to (-2, 1), then the range of f(x) is:

(A) (3, 7)
(B) All positive real numbers
(C) (3, 4)
(D) (4, 7)
(E) (0, 7)

As I had no idea what to do, I simply plugged in the two numbers it gave me (i.e. -2 and 1) into the function, and got out 7 and 4, respectively. Thus I chose to guess with choice D, which has those two numbers.
Unfortunately, my guess was incorrect; the book says that the answer is (A). Can someone please explain to me why this is so and how to correctly go about answering these questions?

Thanks,
Leon

 

[Matt]

Work from the inside out. If the domain is (-2,1), then the

* range of x is (-2,1)

* range of x^2 is [0,4)

* range of x^2 + 3 is [3,7)

 

[stapel]

Hint: Look at the graph of y = x² + 3, considering it only over the interval x = -2 to x = 1. What is the lowest y-value? What is the highest y-value?

Eliz.

 

[lyzhou1990]

thx very much for your help.