graph the exponential function g(x)=4x-1. To do this plot two points on the graph of the function and also draw the asymptote. Additionally give the domain and range of the function using interval notation

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?

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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.

Learn how to graph the exponential function g(x) = 4^(x-1) with detailed steps including plotting points (1, 1) and (2, 4), drawing the horizontal asymptote at y = 0, and determining its domain and range. Understand the exponential growth behavior as x increases. Suitable for high school students.

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