begin with the graph of y = e^x and use transformations to graph the function. determine the domain, range…

begin with the graph of y = e^x and use transformations to graph the function. determine the domain, range, and horizontal asymptote of the function. f(x)= - 2 - e^(-x/2) use the graphing tool to graph the function. (for any answer boxes shown with the grapher, type an exact answer.) what is the domain of f(x)= - 2 - e^(-x/2)? (type your answer in interval notation.)

begin with the graph of y = e^x and use transformations to graph the function. determine the domain, range, and horizontal asymptote of the function. f(x)= - 2 - e^(-x/2) use the graphing tool to graph the function. (for any answer boxes shown with the grapher, type an exact answer.) what is the domain of f(x)= - 2 - e^(-x/2)? (type your answer in interval notation.)

Answer

Explanation:

Step1: Analyze the domain of exponential - type functions

The function (y = f(x)=-2 - e^{-x/2}) is an exponential - type function. The exponential function (y = e^{u}), where (u=-\frac{x}{2}), is defined for all real values of (x). There are no restrictions on the value of (x) that would make the function undefined.

Step2: Write the domain in interval notation

Since there are no values of (x) for which the function (f(x)=-2 - e^{-x/2}) is undefined, the domain of the function is all real numbers. In interval notation, this is ((-\infty,\infty)).

Answer:

((-\infty,\infty))