Question Video: Finding the Sign of a Constant Function | Nagwa Question Video: Finding the Sign of a Constant Function | Nagwa

# Question Video: Finding the Sign of a Constant Function Mathematics • First Year of Secondary School

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In which of the following intervals is π(π₯) = β8 negative? [A] (ββ, 8) [B] (β8, β) [C] (β8, 8) [D] (8, β) [E] (ββ, β)

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### Video Transcript

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.

Letβs 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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