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Must a function that is decreasing over a given interval always be negative over the same interval?Explain

Must a function that is decreasing over a given interval always be negative over the-example-1
User Flooooo
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Final answer:

A decreasing function over a given interval does not necessarily have to be negative over the same interval; it simply means the function's output is becoming smaller as the input increases. It could be always positive, or start positive and then become negative.

Step-by-step explanation:

When we say a function is “decreasing” over a given interval, it means that as we move from left to right along that interval on the x-axis, the value of the function (the y-value) gets smaller. Importantly, the term “decreasing” does not refer to the sign of the function's values, just the behavior of the function as x increases.

For example, a function can be decreasing and still be above the x-axis the entire time (always positive, steadily decreasing). Similarly, a function might start above the x-axis (initially positive) and cross it, becoming negative (becoming negative at the end).

A negative slope indicates a decreasing function, but does not necessarily mean the function is negative. Conversely, a positive slope indicates an increasing function. When the slope is zero, the function is neither increasing nor decreasing; it's constant over that interval.

User Cusejuice
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