Question

use transformations of the graph of ( f(x)=e^{x} ) to graph the given function. be sure to give equations of the asymptotes. use the graphs to determine each functions domain and range. if applicable, use a graphing utility to confirm the hand - drawn graphs.
( h(x)=-e^{x} )
graph ( h(x) ) and its asymptote. graph the asymptote as a dashed line. use the graphing tool to graph the function.
find the equation of the asymptote for ( h(x)=-e^{x} ) using the graph.
( y = 0 )
(type an equation.)
observe the graph and find the domain of ( h(x)=-e^{x} ).
(type your answer in interval notation.)

Explanation:

Step1: Recall domain of exponential function

The function \( h(x) = -e^x \) is an exponential function. The exponential function \( e^x \) is defined for all real numbers \( x \). Multiplying by -1 (a vertical reflection) does not change the set of \( x \)-values for which the function is defined.

Step2: Determine domain in interval notation

Since \( x \) can be any real number, the domain of \( h(x) = -e^x \) is all real numbers. In interval notation, this is \( (-\infty, \infty) \).

Answer:

\((-\infty, \infty)\)