The range takes some analyzing:

Because of the negative coefficient in front of the squared terms, these expressions can also be negative. Check it out: If x is a large number (positive or negative), square what’s in the ()s (now it’s always positive), multiply it by a negative. Now, when you add the 3 or the 5, you still have a large negative number.

Can you see what is the largest y can be? There’s no way that the x term can get positive since it is multiplied by that negative. So, the largest is zero. THEREFORE, the range for the first problem is y<= 5, and the range for the second problem is All Real Numbers, because y > anything from negative infinity to 3.

Hope you get it!

range: (-infinity,5)

2) domain: all integers

range: (-infinity,3)

I don’t understand if ^2 is square root or squared.

Please specify immediately.

y <= -4x^2-11 y > -2x^2 +35