Math Problem Statement

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

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

Solution

As xx approaches 1 from the left (i.e., x1x \to 1^-), the graph of the function g(x)g(x) tends towards a value. Observing the curve of g(x)g(x), it appears that the function approaches the value 3 from the left side of x=1x = 1.

Therefore, as xx gets closer and closer to 1 from the left (but remains less than 1), g(x)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)g(x) as xx approaches 1 from the right?
  2. Is g(x)g(x) continuous at x=1x = 1?
  3. How do you calculate one-sided limits from graphs?
  4. What is the limit of g(x)g(x) as xx approaches 3?
  5. How can you describe the behavior of g(x)g(x) for large negative values of xx?

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

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Math Problem Analysis

Mathematical Concepts

Limits
One-Sided Limits
Graph Analysis

Formulas

Limit notation: \( \lim_{x \to c^-} g(x) \)

Theorems

One-Sided Limit Theorem

Suitable Grade Level

Grades 10-12