Question

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.

Answer 1

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