As \( x \) approaches infinity, which functions \( f(x) \) also approach infinity? Please select three correct answers. Select all that apply: \( \square f(x)=0.4(x+3)(x-5)(2 x-7) \) \( \square f(x)=-6 x(x-1)(x+5)(x+1) \) \( \square f(x)=-3 x(x+7)(x-9) \) \( \square f(x)=0.7(2 x-3)(3 x+5) \) \( \square f(x)=(2 x+8)(x-2)(x+9) \) \( \square f(x)=-2.6(x+8)(x-9)(x+1) \)

To determine which functions \( f(x) \) approach infinity as \( x \) approaches infinity, we observe the behavior of the leading terms in each polynomial. The key is to identify whether the leading coefficient is positive or negative, as positive leading coefficients will lead the function towards infinity. 1. The functions \( f(x)=0.4(x+3)(x-5)(2x-7) \) and \( f(x)=0.7(2x-3)(3x+5) \) exhibit positive leading coefficients, which means they will approach infinity as \( x \) increases toward infinity. 2. In contrast, the other candidates all have negative leading coefficients. For example, \( f(x)=-6x(x-1)(x+5)(x+1) \), \( f(x)=-3x(x+7)(x-9) \), and \( f(x)=-2.6(x+8)(x-9)(x+1) \). These will approach negative infinity as \( x \) approaches infinity. So, the correct answers that approach infinity are: 1. \( \square f(x) = 0.4(x+3)(x-5)(2x-7) \) 2. \( \square f(x) = 0.7(2x-3)(3x+5) \) 3. \( \square f(x) = (2x+8)(x-2)(x+9) \) All three of these last functions have positive leading terms and approach infinity.