Here's the graph of the function \( y = 3^x - \frac{6}{x} \) over the interval \( -2 < x < 2.5 \). The vertical dashed line indicates the asymptote at \( x = 0 \), where the function is undefined.

Would you like a detailed analysis of this graph, or do you have any questions?

Here are 5 related questions that might deepen your understanding:

1. What happens to the function as \( x \) approaches zero from both the left and the right?
2. How does the exponential component \( 3^x \) affect the overall shape of the graph?
3. What are the critical points of this function within the given interval?
4. How does changing the base of the exponential (e.g., from 3 to another number) alter the graph?
5. Can you find the intervals where the function is increasing or decreasing?

**Tip:** When dealing with functions containing both exponential and rational terms, look out for potential vertical asymptotes and sharp changes in behavior around points of division by zero.

y = 3^x - 6/x for -2 < x < 2.5, draw graph

Explore how to graph the function y = 3^x - 6/x over the interval -2 < x < 2.5. Learn about key mathematical concepts, including exponential and rational functions, vertical asymptotes, and graph behavior. Suitable for students in Grades 10-12.

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