Q. 54 - Precalculus Enhanced with Graphing Utilities

Question

Begin with the graph of $y=e^x$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f\left(x\right)=-e^x$

Step-by-Step Solution

Answer

Domain: All real numbers.

Range: $\left\{y|y<0\right\} or \left(-\infty ,0\right)$.

Horizontal asymptote: $y=0$

The graph of the function is given below,

Step 1. Given information.

Consider the given function,

$f\left(x\right)=-e^x$

First, plot the graph of $y=e^x$. Multiply by $-1$ and reflect about x-axis,

Step 2. Determine the characteristics of the function.

Consider the given function,

$f\left(x\right)=-e^x$

From the graph, the domain of the function is the set of all real numbers.

The range is$\left\{y|y<0\right\} or \left(-\infty ,0\right)$.

Horizontal asymptote is $y=0$.