To graph the exponential function $g(x) = 4^x - 1$, we'll go through the following steps:

1. Understand the function:

• The function $g(x) = 4^x - 1$ is an exponential function with a base of 4 and a vertical shift downward by 1 unit.

2. Identify key points:

• Let's find two points on the graph by plugging in specific values for $x$.

  • For $x = 0$: $g(0) = 4^0 - 1 = 1 - 1 = 0$ So, one point is $(0, 0)$.

  • For $x = 1$: $g(1) = 4^1 - 1 = 4 - 1 = 3$ So, another point is $(1, 3)$.

3. Asymptote:

• The horizontal asymptote for the function is $y = -1$. This is because as $x$ approaches negative infinity, $4^x$ approaches 0, making $g(x)$ approach $-1$.

4. Graphing:

• Now, you can plot the points $(0, 0)$ and $(1, 3)$ on the coordinate plane.
• Draw the curve of the exponential function that passes through these points.
• Draw the horizontal asymptote at $y = -1$.

5. Domain and Range:

• Domain: The function $g(x) = 4^x - 1$ is defined for all real numbers $x$, so the domain is $(-\infty, \infty)$.
• Range: Since the function is always greater than $-1$ (because $4^x$ is always positive and shifts downward by 1), the range is $(-1, \infty)$.

Here's a summary of the key points:

• Points: $(0, 0)$ and $(1, 3)$
• Asymptote: $y = -1$
• Domain: $(-\infty, \infty)$
• Range: $(-1, \infty)$

Would you like me to generate a graph of this function for visual reference?