Question

The function f(x) = | x + 2 |can be used to determine how far a number x is away from the number -2 on the number line. Find and interpret the given function values and determine an appropriate domain for the function.

Answer 1

We have the function f(x) = |x+2| that represents the distance of x to the number -2.

For f(-4) we have:

$f(-4)=|-4+2|=|-2|=2$

meaning the number x = -4 is at a distance of 2 units from -2.

This interpretation makes sense in the context of the problem.

For f(0) we have:

$f(0)=|0+2|=|2|=2$

meaning the number x = 0 is at a distance of 2 units from -2.

This interpretation makes sense in the context of the problem.

For f(3.5) we have:

$f(3.5)=|3.5+2|=|5.5|=5.5$

meaning the number x = 3.5 is at a distance of 5.5 units from -2.

This interpretation makes sense in the context of the problem.

We can see that the domain includes numbers that are not integers but rational numbers, like 3.5.

Then the domain is all real numbers.