Correct, but guessing is not really a valid answer. For example, you could say, that this function has a graph that is a parabola, open from below, with highest point . Or you could argue that, since the range of is , the range of must be

No. in fact, for all . - But the correct answer is quite easy to find. Because the range of is and because the exponent 64 is even (and the factor 25 is ), the range of this function must be2. y = 25(-7x-4)^64

I know the domain here is all real numbers.

I am not sure about the range, but am guessing all real numbers <= -100 Is this correct?

This one is more complicated. First the domain is , because for a division by zero would result.3. y = x^2 / (x^2-16)

How would I do this one?

Thanks a bunch

As to the range: consider first the case that . In this case, the numerator is always ( for only), while the denominator is always and tends to 0 from the left (negative side) as x approaches -4 from the right or +4 from the left. So for , this function assumes all values in .

Now consider the second case, namely that or . In this case, the numerator is always positive and larger than the the denominator , and hence the function values are .

From we conclude that for the function values get closer and closer to +1 (from above).

To sum up: the range is .