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As x gets closer and closer to (but stays less than) 1 ,  g(x) gets as close as we want to …

As \( x \) approaches 1 from the left (i.e., \( x \to 1^- \)), the graph of the function \( g(x) \) tends towards a value. Observing the curve of \( g(x) \), it appears that the function approaches the value 3 from the left side of \( x = 1 \).

Therefore, as \( x \) gets closer and closer to 1 from the left (but remains less than 1), \( g(x) \) gets as close as we want to 3.

Would you like any further clarification or details on this?

Here are 5 related questions you might want to explore:

1. What happens to \( g(x) \) as \( x \) approaches 1 from the right?
2. Is \( g(x) \) continuous at \( x = 1 \)?
3. How do you calculate one-sided limits from graphs?
4. What is the limit of \( g(x) \) as \( x \) approaches 3?
5. How can you describe the behavior of \( g(x) \) for large negative values of \( x \)?

**Tip:** When analyzing limits graphically, always check for discontinuities and consider both the left-hand and right-hand

As x gets closer and closer to (but stays less than) 1, g(x) gets as close as we want to…

Learn how to analyze one-sided limits graphically as x approaches 1 in the function g(x). This problem explores key mathematical concepts such as limits and graph analysis. Suitable for students in Grades 10-12.

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