Is it true that without making a graph of an absolute value function, you can describe its position in the coordinate plane? explain with an example.

Yes, it is true.

This an example of how you describe an absolute value function algebraically:

Let the function f(x) be f(x) = |2x + 3|

Find the positive values of the argument: 2x + 3 ≥ 0 => x ≥ -3/2

Then,

f(x) = 2x + 3 for x ≥ -3/2; and

f(x) = -2x - 3 for x < -3/2