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.
(type an equation.)

Explanation:

Step1: Recall transformation of exponential functions

The parent function is \( f(x) = e^x \), which has a horizontal asymptote at \( y = 0 \). The function \( h(x) = -e^x \) is a reflection of \( f(x) = e^x \) over the x - axis.

Step2: Determine the asymptote after transformation

Reflecting a function over the x - axis does not change the horizontal asymptote (since horizontal asymptotes are related to the end - behavior as \( x
ightarrow\pm\infty \), and reflecting over the x - axis affects the sign of the function values but not the horizontal asymptote). So, the horizontal asymptote of \( h(x)=-e^x \) is the same as the horizontal asymptote of \( f(x) = e^x \), which is \( y = 0 \).

Answer:

\( y = 0 \)