Consider the leading term of the polynomial function. What is the end behavior of the graph? 2x⁷ - 8x⁶ - 3x⁵ - 3
The leading term is 2x⁷. Since n is odd and a is positive, the end behavior is up and up.
The leading term is 2x⁷. Since n is odd and a is positive, the end behavior is down and down.
The leading term is 2x⁷. Since n is odd and a is positive, the end behavior is down and up.
The leading term is 2x⁷. Since n is odd and a is positive, the end behavior is up and down.

Solution:

We can define a polynomial as:

P(x) = axⁿ + bx^{n - 1} + …. + c

Where axⁿ is the leading term.

The end behaviour is up and up if n is even and a is positive.

The end behaviour is down and down if n is even and a is negative.

The end behaviour is down and up if n is odd and a is positive.

The end behaviour is up and down if n is odd and a is negative.

It is given that

Polynomial P(x) = 2x⁷ - 8x⁶ - 3x⁵ - 3

Where 2x⁷ is the leading term

a = 2 and n = 7 which is odd.

As n is odd and a is positive, the end behaviour is down and up.

Consider the leading term of the polynomial function. What is the end behavior of the graph? 2x⁷ - 8x⁶ - 3x⁵ - 3

Summary:

Considering the leading term of the polynomial function. The end behavior of the graph 2x⁷ - 8x⁶ - 3x⁵ - 3 is the leading term is 2x⁷. Since n is odd and a is positive, the end behavior is down and up.