Q. 56 - 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.

$f\left(x\right)=e^x-1$

Step-by-Step Solution

Answer

The graph of the function is given below,

Domain: All real numbers.

Range: $\left(-1,\infty \right)$

Horizontal asymptote: $y=-1$

Step 1. Given information.

Consider the given function,

$f\left(x\right)=e^x-1$

First, plot the graph of $y=e^x$, then subtract $1$ and shift down by $1unit$.

Step 2. Determine the characteristics of the function.

Consider the given function,

$f\left(x\right)=e^x-1$

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

We can see $x\to -\infty ,f\left(x\right)\to -1$.

The range is $\left(-1,\infty \right)$.

Horizontal asymptote is $y=-1$.