Question

Identify which of the twelve basic functions listed below fit the deceiption given. 1 | The three functions with end behavior lim f(x) = -10 2 y = x, y= x3, y = int(x) C. y=x2, y = x2, y = int (x) d ==x y=x, y=x2, y = 1 ; y=int (x) 1 +ex

Answer 1

We were given 12 functions and we are to determine which of the 12 functions obey the following rule:

$\lim _{x\to-\infty}f(x)=-\infty$

We will proceed to test how the functions:

$\begin{gathered} f(x)=y \\ \lim _{x\rightarrow-\infty}y=-\infty \\ \\ y=x \\ x\rightarrow-\infty \\ y=-\infty(true\text{)} \\ \\ y=x^3 \\ x\rightarrow-\infty \\ y=(-\infty)^3\Rightarrow-\infty \\ y=-\infty(true\text{)} \\ \\ y=\frac{1}{\mleft(1+e^{-x}\mright)} \\ x\rightarrow-\infty \\ y=\frac{1}{(1+e^{-\infty})}=-\infty \\ y=-\infty(true) \end{gathered}$

Hence, option d is the correct answer