Use the graph of $y=e^{x}$ and transformations to sketch the exponential function $f(x)=-e^{x-7}$. Determine the domain and range. Also, determine the $y$-intercept, and find the equation of the horizontal asymptote.
Use the graphing tool to graph the function.
What is the domain of $f(x)=-e^{x-7} ?$
(Type your answer in interval notation.)
What is the range of $f(x)=-e^{x-7} ?$
(Type your answer in interval notation.)
What is the $y$-intercept of $f(x)=-e^{x-7} ?$
(Simplify your answer. Type an exact answer in terms of e.)

Step 1 ：The function \(f(x)=-e^{x-7}\) is a transformation of the function \(y=e^{x}\). The graph of \(f(x)\) is obtained by shifting the graph of \(y=e^{x}\) 7 units to the right and reflecting it in the x-axis.

Step 2 ：The domain of \(f(x)\) is all real numbers because the exponential function is defined for all real numbers. So, the domain of \(f(x)=-e^{x-7}\) is \((-\infty, \infty)\).

Step 3 ：The range of \(f(x)\) is all real numbers less than 0 because the reflection in the x-axis makes all the y-values negative. So, the range of \(f(x)=-e^{x-7}\) is \((-\infty, 0)\).

Step 4 ：The y-intercept is the value of the function when x=0. We can find this by substituting x=0 into the function. The y-intercept of the function \(f(x)=-e^{x-7}\) is approximately -0.0009118819655545162.

Step 5 ：The horizontal asymptote is the line y=0 because as x approaches negative infinity, the value of the function approaches 0. So, the equation of the horizontal asymptote is \(y=0\).

Step 6 ：\(\boxed{\text{The domain of } f(x)=-e^{x-7} \text{ is } (-\infty, \infty)}\)

Step 7 ：\(\boxed{\text{The range of } f(x)=-e^{x-7} \text{ is } (-\infty, 0)}\)

Step 8 ：\(\boxed{\text{The y-intercept of } f(x)=-e^{x-7} \text{ is approximately } -0.0009118819655545162}\)

Step 9 ：\(\boxed{\text{The equation of the horizontal asymptote is } y=0}\)