Question

Which function is increasing as x approaches negative and positive infinity? select all that apply. select all that apply: f(x)=−2(x 4)(x−3) f(x)=4x(x 1)(x 1)(x 2) f(x)=−1.9(x 5)(x−7)(2x 1) f(x)=(3x 1)(2x−3)(x 7)(x−3) f(x)=−3x^2(4x−1)(3x 1)(x 3)(x 2)

Answer 1

The functions that are increasing as x approaches negative and positive infinity are f(x)=4x(x^1)(x^1)(x^2) and f(x)=(3x^1)(2x−3)(x^7)(x−3).

Step-by-step explanation:

In order to determine which functions are increasing as x approaches negative and positive infinity, we need to analyze the leading term of each function. If the leading term has a positive coefficient, the function will increase as x approaches infinity. On the other hand, if the leading term has a negative coefficient, the function will decrease as x approaches infinity.

Let's analyze the given options:

f(x)=−2(x4)(x−3): The leading term is -2(x4), which has a negative coefficient. Therefore, this function is decreasing as x approaches infinity.

f(x)=4x(x1)(x1)(x2): The leading term is 4x(x1) = 4x2, which has a positive coefficient. Therefore, this function is increasing as x approaches infinity.

f(x)=−1.9(x5)(x−7)(2x1): The leading term is -1.9(x5), which has a negative coefficient. Therefore, this function is decreasing as x approaches infinity.

f(x)=(3x1)(2x−3)(x7)(x−3): The leading term is (3x1) = 3x, which has a positive coefficient. Therefore, this function is increasing as x approaches infinity.

f(x)=−3x2(4x−1)(3x1)(x3)(x2): The leading term is -3x2, which has a negative coefficient. Therefore, this function is decreasing as x approaches infinity.

Based on the analysis of the leading terms, the functions that are increasing as x approaches negative and positive infinity are:

f(x)=4x(x1)(x1)(x2)

f(x)=(3x1)(2x−3)(x7)(x−3)