Question: The range of the function f(x) = |x - 1| is:
Options:
(-∞, 1)
[0, ∞)
(-1, 1)
[1, ∞)
Correct Answer: [0, ∞)
Solution:
The absolute value function has a minimum value of 0, hence the range is [0, ∞).
The range of the function f(x) = |x - 1| is:
Practice Questions
Q1
The range of the function f(x) = |x - 1| is:
(-∞, 1)
[0, ∞)
(-1, 1)
[1, ∞)
Questions & Step-by-Step Solutions
The range of the function f(x) = |x - 1| is:
Step 1: Understand the function f(x) = |x - 1|. This is an absolute value function.
Step 2: Know that the absolute value of any number is always 0 or positive.
Step 3: Find the minimum value of the function. The minimum occurs when x - 1 = 0, which is when x = 1. At this point, f(1) = |1 - 1| = |0| = 0.
Step 4: Since the absolute value can only be 0 or greater, the function will never produce a negative value.
Step 5: Therefore, the smallest value of f(x) is 0, and it can go up to infinity as x moves away from 1 in either direction.
Step 6: Conclude that the range of the function is all values from 0 to infinity, written as [0, ∞).
Absolute Value Function – The absolute value function outputs the non-negative distance of a number from zero, which means it cannot be negative.
Range of a Function – The range of a function is the set of all possible output values, which in this case is determined by the minimum value of the absolute value function.
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