Here is the graph of the exponential function $g(x) = 4^{x-1}$:

• The red points $(1, 1)$ and $(2, 4)$ are plotted on the graph.
• The green dashed line represents the horizontal asymptote at $y = 0$.
• The curve shows the exponential growth as $x$ increases.

Domain and Range:

• Domain: $(-\infty, \infty)$
• Range: $(0, \infty)$

Do you have any questions or need more details?

---

Here are 5 related questions:

1. What is the effect of changing the base from 4 to 2 in the function?
2. How does the graph change if the function is $g(x) = 4^{x+1}$?
3. What happens to the graph if we introduce a vertical shift, such as $g(x) = 4^{x-1} + 2$?
4. How would you graph $g(x) = -4^{x-1}$, and what are its properties?
5. How can you determine the y-intercept of an exponential function like $g(x) = 4^{x-1}$?

Tip: When graphing functions, plotting a few key points and identifying asymptotes helps to accurately sketch the overall shape.