SOLUTION: Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. y=3-x^2

Question 698361: Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. y=3-x^2
Answer by Positive_EV(69) (Show Source): You can put this solution on YOUR website!
A function can be bounded by one of two criteria:

1) A variable cannot cause a denominator to equal 0,
2) A variable cannot cause a value under a square root (or any even-powered root) to be negative.

In the original equation, you can use these rules to find any bounds on the domain, or x-values, of the function, since it is in the form y = f(x). There's no fractions and no radicals to worry about, so the domain is unbounded.

To find if there are bounds on y, you must solve the original equation for x in terms of y, or x = f(y).

(note, the 0 here is not needed, I have it here so the +/- symbol works right).

Now that you have x in terms of y, there is a y under a square root sign. The y-values are thus bounded by the expression under the square root needing to be non-negative.

3 - y >= 0
3 >= y

Thus, y is bounded in that it cannot be larger than 3.
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