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=(1)/(\mleft(1+e^(-x)\mright)) \\ x\rightarrow-\infty \\ y=(1)/((1+e^(-\infty)))=-\infty \\ y=-\infty(true) \end{gathered}`

Hence, option d is the correct answer