part 1 of 4\nuse transformations of the graph of f(x)=e^x to graph the given function. be sure to give the…

part 1 of 4\nuse transformations of the graph of f(x)=e^x to graph the given function. be sure to give the equation of the asymptote. use the graph to determine the functions domain and range. g(x)=e^(x - 5)\ngraph g(x)=e^(x - 5). use the graphing tool to graph the function.\nclick to enlarge graph

part 1 of 4\nuse transformations of the graph of f(x)=e^x to graph the given function. be sure to give the equation of the asymptote. use the graph to determine the functions domain and range. g(x)=e^(x - 5)\ngraph g(x)=e^(x - 5). use the graphing tool to graph the function.\nclick to enlarge graph

Answer

Explanation:

Step1: Analyze transformation

The function $g(x)=e^{x - 5}$ is a horizontal - shift of $f(x)=e^{x}$ to the right by 5 units.

Step2: Find the asymptote

The exponential function $y = e^{x}$ has a horizontal asymptote $y = 0$. Shifting it horizontally does not change the asymptote. So, the asymptote of $g(x)=e^{x - 5}$ is $y = 0$.

Step3: Determine the domain

The domain of the exponential function $y = e^{x}$ is all real numbers. A horizontal shift does not change the domain. So, the domain of $g(x)=e^{x - 5}$ is $(-\infty,\infty)$.

Step4: Determine the range

The range of the exponential function $y = e^{x}$ is $(0,\infty)$. A horizontal shift does not change the range. So, the range of $g(x)=e^{x - 5}$ is $(0,\infty)$.

Answer:

Asymptote: $y = 0$; Domain: $(-\infty,\infty)$; Range: $(0,\infty)$