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Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasing?

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7 votes

Answer:

A.

Explanation:

User Samuel Hulla
by
8.5k points
4 votes
f(x) = -(x + 8)² - 1

The function (not its graph) decreases on interval [-8, ∞). It is a quadratic function in vertex form. That form makes it easy to pick out the one extremum, where x equals -8. The leading coefficient is negative, so the extremum must be a maximum. The function decreases as x increases from there.

Notice that I include the value -8 in the interval. The function does not have instantaneous decrease at that value, but that is not what it means for a function to be decreasing over an interval.

Let a and b be any two values on [-8, ∞), such that a < b.

-8 ≤ a < b

Then f(a) > f(b). Therefore, function f is decreasing on interval [-8, ∞).
User Andreadi
by
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