Question

Given the function f(x)=0.2(x−2)(x+1)(x−5) determine the end behavior of the function.

Select the correct answer below:
A. as x→[infinity],f(x)→−[infinity]
as x→−[infinity],f(x)→[infinity]

B. as x→[infinity],f(x)→[infinity]
as x→−[infinity],f(x)→−[infinity]

C. as x→±[infinity],f(x)→[infinity]

D. as x→±[infinity],f(x)→−[infinity]

Answer 1

The end behavior of the function f(x) = 0.2(x-2)(x+1)(x-5) is as x approaches positive or negative infinity, f(x) approaches positive infinity.

Step-by-step explanation:

The end behavior of a function can be determined by analyzing the leading term of the function. In this case, the leading term of the function f(x) = 0.2(x-2)(x+1)(x-5) is 0.2x^3. Since the leading term has an odd degree and a positive coefficient, the end behavior of the function is as x approaches positive or negative infinity, f(x) approaches positive infinity.

So, the correct answer is B. as x→[infinity],f(x)→[infinity] as x→−[infinity],f(x)→−[infinity]