Find the End Behavior f(x)=X^7

The function declaration ${\displaystyle f\left(x\right)}$ varies according to ${\displaystyle x}$, but the input function ${\displaystyle X^7}$ only contains the variable ${\displaystyle X}$. Assume ${\displaystyle f\left(X\right)=X^7}$.

The largest exponent is the degree of the polynomial.

Since the degree is odd, the ends of the function will point in the opposite directions.

Odd

Since the leading coefficient is positive, the graph rises to the right.

Positive

Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior.

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

Determine the behavior.

Falls to the left and rises to the right