- f(-5) = -8, meaning the number -5 is a distance of 8 units away from 3 on the number line. This interpretation -5 is left of 3 in the context of the problem.
- f(1) = -8, meaning the number 1 is a distance of 2 units away from 3 on the number line. This interpretation 2 is left of 3 in the context of the problem.
- f(1.5) = -8, meaning the number 1.5 is a distance of 1.5 units away from 3 on the number line. This interpretation 1.5 is left of 3 in the context of the problem.
- Based on the observation above, it is clear that an appropriate domain for the function is all real numbers.
What is a number line?
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
How to find and interpret the given function values?
Given the following function; f(x) = |x - 3|.
When x = -5, we have:
f(-5) = |-5 - 3|
f(-5) = |-8| = 8.
f(-5) = -8, meaning the number -5 is a distance of 8 units away from 3 on the number line. This interpretation -5 is left of 3 in the context of the problem.
When x = 1, we have:
f(1) = |1 - 3|
f(1) = |-2| = 2.
f(1) = -8, meaning the number 1 is a distance of 2 units away from 3 on the number line. This interpretation 2 is left of 3 in the context of the problem.
When x = 1.5, we have:
f(1.5) = |1.5 - 3|
f(1.5) = |-1.5| = 1.5.
f(1.5) = -8, meaning the number 1.5 is a distance of 1.5 units away from 3 on the number line. This interpretation 1.5 is left of 3 in the context of the problem.
Based on the observation above, it is clear that an appropriate domain for the function is all real numbers.
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Complete Question:
The function f(x) = |x - 3| can be used to determine how far a number x is away from the number 3 on the number line. Find and interpret the given function values and determine an appropriate domain for the function.
