What are the end behaviors of f(x) = (x + 2)6?A.Both ends go up.B.The left end goes down; the right end goes up.C.The left end goes up; the right end goes down.D.Both ends go down.SUBMITarrow_backPREVIOUS
Question
What are the end behaviors of f(x) = (x + 2)6?A.Both ends go up.B.The left end goes down; the right end goes up.C.The left end goes up; the right end goes down.D.Both ends go down.SUBMITarrow_backPREVIOUS
Solution
The end behavior of a function is determined by the degree and the leading coefficient of the polynomial.
In the given function f(x) = (x + 2)^6, the degree of the polynomial is 6, which is an even number.
For polynomials with an even degree, both ends of the graph will go in the same direction.
The leading coefficient is 1 (since there is no number in front of (x + 2)^6, it is understood to be 1), which is positive.
For polynomials with a positive leading coefficient, the right end of the graph will go up.
Therefore, since both ends of the graph go in the same direction and the right end goes up, the left end also goes up.
So, the end behavior of f(x) = (x + 2)^6 is: Both ends go up.
So, the answer is A. Both ends go up.
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