SOLUTION: The domain of the function q(x) = x^4 + 4x^2 + 4 is [0,\infty). What is the range? No matter what, I can't seem to get the right answer.

Question 1169641: The domain of the function q(x) = x^4 + 4x^2 + 4 is [0,\infty). What is the range?
No matter what, I can't seem to get the right answer.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
sketch it:

y-axis intersected at -> point (,)
if given that the domain of the function is
[,)

then the range is: { element : }
in interval notation: [,)
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Since the original expression is the square of a real number, the original expression is always greater than or equal to 0.

is always 2 or greater, because alone is always 0 or greater.

Then, since the minimum value of is 2, the minimum value of is

ANSWER: The range of is [4,infinity).

An even easier path to that answer is to note that both and are always 0 or greater (with the minimum value of both at x=0); that means the minimum value of is 0+0+4 = 4.

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