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.

Answer

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Answer

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

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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.

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.

Answer

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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.