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:
as $x \rightarrow \infty, f(x) \rightarrow-\infty$
as $x \rightarrow-\infty, f(x) \rightarrow \infty$
as $x \rightarrow \infty, f(x) \rightarrow \infty$
as $x \rightarrow-\infty, f(x) \rightarrow-\infty$
as $x \rightarrow \pm \infty, f(x) \rightarrow \infty$
as $x \rightarrow \pm \infty, f(x) \rightarrow-\infty$
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Content attribution

Step 1 ：The end behavior of a function is determined by the degree and the leading coefficient of the polynomial. The degree of the given function is 3 (since it's a cubic function) and the leading coefficient is 0.2. Since the degree is odd and the leading coefficient is positive, as x approaches positive infinity, the function approaches positive infinity and as x approaches negative infinity, the function approaches negative infinity.

Step 2 ：\(f = (0.2x - 0.4)(x - 5)(x + 1)\)

Step 3 ：\(\lim_{{x \to \infty}} f(x) = \infty\)

Step 4 ：\(\lim_{{x \to -\infty}} f(x) = -\infty\)

Step 5 ：\(\boxed{\text{As } x \rightarrow \infty, f(x) \rightarrow \infty \text{ and as } x \rightarrow-\infty, f(x) \rightarrow-\infty}\)