Chapter 3, Problem 18RE

Solution

To graph: Graph the function $f\left(x\right)=\frac{100}{4+2e^{–0.01x}}$ , and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior.

Given information: The function $f\left(x\right)=\frac{100}{4+2e^{–0.01x}}$ .

Graph:

The given function is- $f\left(x\right)=\frac{100}{4+2e^{–0.01x}}$

  

Interpretation:

Domain: All real $x$ .

Range: All real $y$ such that $0<y<25$ .

Continuity: Function is continuous on its domain.

Increasing or decreasing behavior: Function is increasing on its domain.

Symmetry: Function is not containing any symmetry.

Bounded: Function is bounded below at $y=0$ and above $y=25$ .

Extrema: Function has no one extrema.

Asymptotes: Function has two horizontal asymptote at $y=0$ and $y=25$ .

End behavior: $\underset{x\to -\infty }{\lim }f\left(x\right)=0$ and $\underset{x\to \infty }{\lim }f\left(x\right)=25$ .