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In which of the following intervals is π(π₯) = β8 negative? [A] (ββ, 8) [B] (β8, β) [C] (β8, 8) [D] (8, β) [E] (ββ, β)

In which of the following intervals is π of π₯ equal to negative eight negative? Is it (A) the open interval from negative β to eight? (B) The open interval from negative eight to β. (C) The open interval from negative eight to eight. (D) The open interval from eight to β. Or (E) the open interval from negative β to β.

Letβs begin by considering what the function π of π₯ equals negative eight looks like. If we consider the normal coordinate axes, our horizontal axis is the π₯-axis and our vertical one is the π¦-axis. The π¦-axis can be replaced in this case with π of π₯. We are told that π of π₯ is equal to negative eight. Therefore, we need to find negative eight on the π¦- or π of π₯ axis. Our function is a horizontal line through this point. This line will continue indefinitely to the left and to the right. As the line is entirely below the π₯-axis, it will always be negative. As π of π₯ equal to negative eight is always negative, the correct answer is option (E) the open interval negative β to β. If any function is equal to a constant, it will always just have one sign. In this case, the function is always negative.

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