Question

Graphing Exponential Functions Graph the function, not by plotting points, but by starting from the graph of $y=e^x$in Figure 1. State the domain, range, and asymptote.

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

Short answer

The graph is:

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

The range is $\left(-\infty ,0\right)$.

The horizontal asymptote is $y=0$.

Step-by-step solution

Step 1. Given.

The given function is $f\left(x\right)=-e^x$.

Step 2. To determine.

We have to graph the given function, not by plotting points, but by starting from the graph of$y=e^x$ in Figure 1. Then we have to state the domain, range, and asymptote.

Step 3. Calculation.

The parent function of $f\left(x\right)=-e^x$is $y=g\left(x\right)=e^x$.

So,

$$\begin{gathered} f\left(x\right)=-e^x \\ =-g\left(x\right) \end{gathered}$$

It means we will reflect$y=e^x$ over the x-axis to graph $f\left(x\right)=-e^x$.

Therefore, the graph is:

The possible x-values are all real numbers. So, the domain is $\left(-\infty ,\infty \right)$.

The y-values are from$-\infty$ to 0. So, the range is $\left(-\infty ,0\right)$.

From the graph the horizontal asymptote is $y=0$.