Question

question #1
describe the leading coefficient of the polynomial function given its graph below.
the leading coefficient is negative because the left arrow is pointing downwards.
the leading coefficient is positive because the left arrow is pointing downwards.
the leading coefficient is negative because the right arrow is pointing upwards.
the leading coefficient is positive because the right arrow is pointing upwards.

Explanation:

Step1: Recall end - behavior rule

For a polynomial function \(y = a_nx^n+\cdots+a_0\), if \(n\) is even and \(a_n> 0\), the graph goes up on both ends; if \(n\) is even and \(a_n < 0\), the graph goes down on both ends; if \(n\) is odd and \(a_n>0\), the graph goes down on the left and up on the right; if \(n\) is odd and \(a_n < 0\), the graph goes up on the left and down on the right.

Step2: Analyze the graph

The left - hand side of the graph is pointing downwards and the right - hand side is pointing upwards. This is the end - behavior of an odd - degree polynomial with a positive leading coefficient.

Answer:

The leading coefficient is positive because the right arrow is pointing upwards.