Final answer:
The range of the function f(x) = |x| is anytime y is greater than or equal to 0, represented as y . This is because the absolute value function is always non-negative.
Step-by-step explanation:
The function f(x) = |x|, also known as the absolute value function, depicts a V-shaped graph that opens upwards. Its lowest point, or vertex, is at the origin (0,0). The y-values, or the values of f(x), are always 0 or greater regardless of the x-values. Therefore, the range of the function f(x) = |x| is all y such that y is greater than or equal to 0. This is represented as 0 ≤ y < ∞. In other words, for any x in the entire set of real numbers from -∞ to ∞, the value of |x| will always be non-negative.
Remember that the range refers to the set of all possible output values (y-values) of a function, given the entire set of input values (x-values).
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