Chapter 6, Problem 3CT

To determine

To graph : the equation and state the domain, range and asymptote of the equation

Explanation of Solution

Given information The equation is $y=4e^{-2x}$

Concept used:

The domain of a function is defined as the set of all values of $x$ for which the function is defined.

The range of a function is defined as the set of all values that the function $y=f\left(x\right)$ takes.

An asymptote of a function is a lines such that the distance between the curve of the function and the line approaches zero as one or both of the $x\text{ or }y$ coordinates tends to infinity.

Graph :

The equation is $y=4e^{-2x}$

Use graphing calculator to graph the function, $y=4e^{-2x}$

Therefore the graph is obtained as:

  

Interpretation: from the above graph it can be observed that the domain is $x\in \left(-\infty ,\infty \right)$ and $y\in \left[0,\infty \right)$ respectively and horizontal asymptote is $y=0$ and vertical asymptote is $x=-1$ .