Determine the end behavior of the function:f(x)=x3+1

Question

BlackTom AI · Accepted Answer

We are asked to determine the end behavior of the function f(x) = x^3 + 1.
First, recall that for polynomials, the end behavior is governed by the leading term, which here is x^3, since lower-degree terms become negligible as |x| becomes large.
As x → -∞, the leading term x^3 → -∞, so f(x) → -∞ (the graph goes downward on the far left).
As x → ∞, the leading term x^3 → ∞, so f(x) → ∞ (the graph goes upward on the far right).
Therefore, the end behavior is down to the left and up to the right.
This matches the provided option: 'Down to the left and up to the right'.

ALGII141-027 4.1 Practice Problems

Determine the end behavior of the function:f(x)=x3+1

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