Answer
a. The graph falls to the left and rises to the right
b. No
c. The graph falls to the left and right
d. Yes
Work Step by Step
Case - End Behavior of graph
When n is odd and an is positive, the graph falls to the left and rises to the right.
When n is odd and an is negative, the graph rises to the left and falls to the right.
When n is even and an n is positive, the graph rises to the left and right.
When n is even and n is negative, the graph falls to the left and right
$f(x)=158x^3-2845x^2+12926x+7175$
$g(x)=-17x^4+508x^3-5180x^2+18795x+2889$
a. for $f(x)$, the leading coefficient is positive and the degree of the function is odd, therefore, the graph falls to the left and rises to the right.
b. NO, from the leading coefficient test of $f(x)$ we can see that the graph of $f(x)$ rises to the right. But that is not the case for the graph of Amazon deforestation if the Amazon rainforest cutdown continues to decline.
c. For $g(x)$, the leading coefficient is negative and the degree of the function is even. Therefore, the graph falls to the left and right
d. YES, from the leading coefficient test of $g(x)$ we can see that the graph of $g(x)$ falls to the left and right. If the rate at which the Amazon rainforest is being cut down continues to decline, the $g(x)$ will be useful to model it.
