Based on the observations below, it is clear that an appropriate domain for the function, .f(x) = |x - 3|, is: {-5, 1, 1.5}.
What is the Domain of a Function?
The set of corresponding x-values of a function can be defined as the domain of the function.
We are given the function, .f(x) = |x - 3|, which we are to use to determine how far "x", which is a number is away from 3 on a number line.
f(-5) = |-5 - 3| = 8. This means the number, -5, is a distance of 8 units away from 3 on the number line.
f(1) = |1 - 3| = 2. This means the number, 1, is a distance of 2 units away from 3 on the number line.
f(1.5) = |1.5 - 3| = 1.5. This means the number, 1.5, is a distance of 1.5 units away from 3 on the number line.
Therefore, based on the above observations, it is clear that an appropriate domain for the function, .f(x) = |x - 3|, is: {-5, 1, 1.5}.
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