How do you solve for the RANGE for this piecewise function?

Question

Here's the pre-calculus problem I got:

f(x) = { x^2 +3 for x < 0

(4x - x^2) / (x - 4) for x > 2

Identify the domain and range.

I figured out the domain, but my range does not match up with the range my teacher had on the answer sheet.

My range was (- infinity, -2) U (3, infinity) ...but this is wrong.

Please help!

Answer 1

You almost have the correct range here.

First, your (3, infinity) is correct.

Second, ask yourself &quot;How did I come up with (-infinity, -2)?&quot;

Placing 2 inside (4x - x^2)/(x - 4) gives us (8 - 4)/(2 - 4) = - 2.

And f(x) appoaches negative infinity as x approaches positive infinity.

But, we have a denominator, x - 4, and denominators can never equal zero.  You should be able to find the correct range now.