Question

Select the graph and the description of the end behavior of f(x) = −x3 + 2.

This is a cubic function. The end behavior of the graph will decrease to the right and increase to the left.

This is a cubic function. The end behavior of the graph will increase to the right and decrease to the left.

This is a cubic function. The end behavior of the graph will increase to the right and decrease to the left.

This is a cubic function. The end behavior of the graph will decrease to the right and increase to the left.

Answer 1

Answer: D

Explanation:

End behavior is determined by two factor:

1. Coefficient - determines right side:

• If the leading coefficient is POSITIVE, then right side goes to +∞
• If the leading coefficient is NEGATIVE, then right side goes to -∞

2. Degree - determines left side:

• If degree is EVEN, then left side is SAME as right side
• If degree is ODD, then left side is OPPOSITE of right side

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-x³ + 2

Leading coefficient is NEGATIVE, so right side goes to -∞ (decreases)

Degree is ODD, so left side is opposite of right side → goes to +∞ (increases)