Below is the graph of $y=e^{x}$.
Transform it to make the graph of $y=e^{x+6}-2$.
Give the domain and range of $y=e^{x+6}-2$ using interval notation.

Step 1 ：The transformation of the graph \(y=e^{x}\) to \(y=e^{x+6}-2\) involves two steps. First, the graph is shifted to the left by 6 units. This is represented by the \(+6\) inside the exponent. Then, the graph is shifted down by 2 units. This is represented by the \(-2\) outside the exponent.

Step 2 ：The domain of the function \(y=e^{x+6}-2\) is all real numbers because the exponential function is defined for all real numbers.

Step 3 ：The range of the function \(y=e^{x+6}-2\) is all real numbers greater than \(-2\). This is because the exponential function \(e^{x}\) is always positive, so \(e^{x+6}\) is also always positive. When we subtract 2, the smallest value the function can take is \(-2\).

Step 4 ：Final Answer: The domain of the function \(y=e^{x+6}-2\) is all real numbers, which in interval notation is \((-\infty, \infty)\). The range of the function is all real numbers greater than \(-2\), which in interval notation is \((-2, \infty)\). So, the domain is \(\boxed{(-\infty, \infty)}\) and the range is \(\boxed{(-2, \infty)}\).