The given function is $g(x) = 3^x - 3$. The y-intercept of $g(x)$ occurs at $x = 0$:

$g(0) = 3^0 - 3 = 1 - 3 = -2$

To make the y-intercept equal to 0, the graph must be vertically shifted up by 2 units (since the current y-intercept is at $-2$). Adding 2 to $g(x)$ results in the modified function:

$h(x) = g(x) + 2 = 3^x - 3 + 2 = 3^x - 1$

Thus, the equation for the modified graph, where the y-intercept is 0, is:

$h(x) = 3^x - 1$

Explanation:

• The transformation involves a vertical shift.
• The value added ($+2$) compensates for the original y-intercept ($-2$) to ensure the new intercept is 0.

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Would you like a graphical illustration or further breakdown?
Here are 5 related questions for practice:

1. What is the domain and range of $g(x) = 3^x - 3$?
2. How does the horizontal asymptote change for the function $h(x) = 3^x - 1$?
3. What transformations occur when $g(x)$ is modified to $h(x) = 3^x - 1$?
4. What is the y-intercept of $2 \cdot g(x)$?
5. Find the x-intercept of $h(x) = 3^x - 1$.

Tip: To modify intercepts, adjust the constant term of the function.