Problem

What are the end behaviors of $f(x)=-2(x-2)^{5}$ ? A. Both ends go down. B. Both ends go up. C. The left end goes down; the right end goes up. D. The left end goes up; the right end goes down.

Solution

Step 1 :The end behavior of a function is determined by the degree and the leading coefficient of the polynomial. The degree of the polynomial is 5, which is odd, and the leading coefficient is -2, which is negative.

Step 2 :For polynomials with an odd degree and a negative leading coefficient, the left end of the graph goes up and the right end of the graph goes down.

Step 3 :So, the final answer is D. The left end goes up; the right end goes down.

From Solvely APP
Source: https://solvelyapp.com/problems/28673/

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