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Eddie S.

asked • 03/29/14

What is the range of this function?

f(x)=2 sqr(-x^2+4) - 2
the range is R:{y| -2 ≤ y ≤ 2, yER)
How do i get this answer?

1 Expert Answer

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Steve S. answered • 03/30/14

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5 (3)

Tutoring in Precalculus, Trig, and Differential Calculus

Eddie S.

How do you know that 4 – x^2 will be maximum when x = 0 and 4 – x^2 will be minimum when x = ±2?
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03/30/14

Steve S.

Because y = 4 – x^2 is a parabola that opens down. It's x-intercepts are ±2 so it's maximum is halfway between at x = 0. It's minimum on the domain –2 ≤ x ≤ 2 is when it is zero at x = ±2.
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03/30/14

Eddie S.

But doesn't this square root function go continuously to the left and starts at -2? So why would there be 2 zeros and a vertex?
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03/30/14

Steve S.

See revised answer.
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03/31/14

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