Question

Given the function

f(x)=0.2(x−2)(x 1)(x−5).

Determine the end behavior of the function.

Answer 1

The end behavior of the function is as follows: As x approaches negative infinity, f(x) approaches positive infinity. As x approaches positive infinity, f(x) approaches positive infinity.

Step-by-step explanation:

The end behavior of a function is determined by the leading term of the function's equation. In this case, the leading term is 0.2(x−2)(x 1)(x−5). Since the degree of the polynomial is 3, and the leading coefficient is positive, the end behavior is as follows:

• As x approaches negative infinity, f(x) approaches positive infinity.
• As x approaches positive infinity, f(x) approaches positive infinity.