The function f(x) = |x - 3| is continuous at which of the following points?

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Q: The function f(x) = |x - 3| is continuous at which of the following points?

Solution: The function |x - 3| is continuous everywhere, including at x = 3.

Steps: 7

Step 1: Understand what the function f(x) = |x - 3| means. It represents the distance between x and 3 on a number line.
Step 2: Recall the definition of continuity. A function is continuous at a point if you can draw it without lifting your pencil.
Step 3: Identify the points we need to check for continuity. In this case, we are checking at x = 3 and other points.
Step 4: Analyze the function |x - 3|. It is made up of two parts: when x is less than 3 (the function is -(x - 3)) and when x is greater than or equal to 3 (the function is (x - 3)).
Step 5: Check the behavior of the function as x approaches 3 from both sides. As x gets closer to 3 from the left, f(x) approaches 0, and as x approaches from the right, f(x) also approaches 0.
Step 6: Since the function approaches the same value (0) from both sides at x = 3, it is continuous at that point.
Step 7: Since the function |x - 3| is a simple absolute value function, it is continuous everywhere on the number line, not just at x = 3.