Identify which of the twelve basic functions listed below fit the description given.
-The four functions that are increasing on the interval $( - \infty , 0 )$
A) $y = x , y = x ^ { 3 } , y = x ^ { 2 } , y = e ^ { x }$
B) $y = x , y = x ^ { 3 } , y = e ^ { x } , y = \frac { 1 } { 1 + e ^ { - x } }$
C) $y = x , y = x ^ { 3 } , y = x ^ { 2 } , y = \frac { 1 } { 1 + e ^ { - x } }$
D) $y = x ^ { 3 } , y = \frac { 1 } { x } , y = | x | , y = x$

Question

Quizplus · Accepted Answer

Functions $y = x$, $y = x^3$, and $y = e^x$ are increasing on the interval $(- \infty, 0)$ because their derivatives are positive. The function $y = \frac{1}{1 + e^{-x}}$ is the logistic function, which is also increasing on $(- \infty, 0)$ as its derivative is positive in this interval.

Identify Which of the Twelve Basic Functions Listed Below Fit (−∞,0)( - \infty , 0 )(−∞,0)

Identify Which of the Twelve Basic Functions Listed Below Fit $( - \infty , 0 )$