Answer:
The graph falls to the left and rises to the right.
Explanation:
Given f(x) defined below:
[tex]f\mleft(x)=(x+1)(x+4)(x+5)^5\mright?[/tex]We are to determine the end behavior of the polynomial using the Leading Coefficient Test.
When using the Leading coefficient test, the following rule applies:
• When the ,degree is odd, and the ,leading coefficient is positive,, the graph falls to the left and rises to the right.
,• When the ,degree is odd, and the ,leading coefficient is negative,, the graph rises to the left and falls to the right.
,• When the ,degree is even, and the ,leading coefficient is positive,, the graph rises to the left and right.
,• When the ,degree is even, and the ,leading coefficient is negative,, the graph falls to the left and right.
Back to our function, f(x):
[tex]\begin{gathered} f(x)=(x+1)(x+4)(x+5)^5 \\ \text{Degree}=7\text{ (Odd)} \\ \text{Leading Coefficient = 1 (Positive)} \end{gathered}[/tex]From the first rule above, we can conclude that the graph falls to the left and rises to the right.
A graph of f(x) is attached which confirms this end behavior.
