To solve the given problem, we need to determine the domain and range of the exponential function shown in the graph.

Observations:

1. Horizontal Asymptote: The graph approaches $y = -6$ but never crosses it.

2. Domain:

   • The graph extends infinitely to the left and right along the $x$-axis.
   • This means the domain includes all real numbers.
   • Domain: $x \in (-\infty, \infty)$.

3. Range:

   • The graph is above $y = -6$ for all $x$, but it never touches $y = -6$.
   • Thus, the range is $y > -6$.
   • Range: $y \in (-6, \infty)$.

Final Answer:

(a) Domain: $x \in (-\infty, \infty)$ (or "All reals")
(b) Range: $y > -6$

Would you like further explanation or a related concept clarified?

Related Questions:

1. What is an exponential function, and how does it behave?
2. How does the horizontal asymptote influence the range of an exponential function?
3. Can an exponential function have a different domain than $(-\infty, \infty)$?
4. How do transformations (e.g., vertical shifts) affect the graph of an exponential function?
5. How can we identify the horizontal asymptote from an equation of an exponential function?

Tip:

The domain of most exponential functions is $(-\infty, \infty)$, while the range depends on vertical transformations!