Algebra-2

From the graph, it can be seen that as and as . The ends go in the same direction, we can conclude that the curve must have:

1.Leading Coefficient: Negative

2.Degree: Even

This is because a polynomial with a negative leading coefficient and an even degree will have both ends of the graph going to ().

 

End Behavior Analysis

Negative Leading Coefficient: This indicates that as ( x ) approaches positive or negative infinity, the values of ( y ) will decrease indefinitely.

 

Even Degree: This ensures that the ends of the graph will move in the same direction (both downward in this case).

 

Matching Equation from Provided Options

Now, let’s reaffirm the equations you provided and analyze them in light of the conclusion:
A.

Leading Coefficient: Positive (1)

Degree: Odd (3)

Conclusion: Does not match.

 

B.