Which of the following is the range of the function f(x) = |x - 1|?

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Question: Which of the following is the range of the function f(x) = |x - 1|?

Options:

Correct Answer: [0, ∞)

Solution:

The minimum value of |x - 1| is 0 when x = 1, so the range is [0, ∞).

Which of the following is the range of the function f(x) = |x - 1|?

Which of the following is the range of the function f(x) = |x - 1|?

Step 1: Understand the function f(x) = |x - 1|. This means we are looking at the absolute value of (x - 1).
Step 2: Recall that the absolute value of a number is always non-negative. This means |x - 1| will always be 0 or positive.
Step 3: Find the minimum value of |x - 1|. This occurs when x - 1 = 0, which happens when x = 1.
Step 4: Calculate |1 - 1|. This equals |0|, which is 0. So, the minimum value of the function is 0.
Step 5: Since |x - 1| can increase without bound as x moves away from 1, the maximum value is infinity.
Step 6: Combine the minimum and maximum values to determine the range. The range is from the minimum value (0) to infinity (∞).
Step 7: Write the range in interval notation: [0, ∞).

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