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What happens to the graph of y=−x^3−5x^2−3x+9 as x heads toward ∞ and −∞ ?

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Answer and explanation:

Behavior of the graph as x approaches ∞:

As x approaches ∞, the graph falls to the right (i.e., y decreases while x increases).

Behavior of the graph as x approaches − ∞:

As x approaches − ∞, the graph rises to the left (i.e., y increases while x decreases)

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For a visual reference, I attached a graph from Desmos that shows how:

  • x increases and y decreases as x approaches ∞ (aka, as x increases/gets bigger towards the end of the cubic curve, since we only consider the end behavior as x approaches ∞ and −∞),
  • and x decreases and y increases as x approaches − ∞ (aka, as x decreases/gets smaller).
  • I also added some points from the graph to further emphasize this end behavior of x and y.

What happens to the graph of y=−x^3−5x^2−3x+9 as x heads toward ∞ and −∞ ?-example-1
User Florent Cardot
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