Determine the end behavior of the function:f(x)=−2x3+1

Question

BlackTom AI · Accepted Answer

The problem asks to determine the end behavior of the function f(x) = −2x^3 + 1.
First, observe the leading term: −2x^3. The degree is 3 (an odd degree) and the leading coefficient is negative.
For cubic functions with a negative leading coefficient, the end behavior is opposite on the two ends: as x approaches negative infinity, the x^3 term tends to negative infinity, and multiplying by −2 flips that to positive infinity; as x approaches positive infinity, the x^3 term tends to positive infinity, and multiplying by −2 keeps it negative infinity.
Concretely:
- When x → −∞, x^3 → −∞, so −2x^3 → ∞.
- When x → ∞, x^3 → ∞, so −2x^3 → −∞.
Therefore, the end behavior is up to the left and down to the right.
Note: In the provided data, there are no answer choices listed to evaluate; the conclusion above explains the correct end behavior based on the polynomial's leading term and degree.

ALGII141-027 Unit 4 Test

Determine the end behavior of the function:f(x)=−2x3+1

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