Question

The graph shown is the solution set for which of the following inequalities?

y < x - 3
y < |x| - 3
y < |x + 3|

Answer 1

The inequality is y < l x+3 l

Answer 2

The inequality that represent the given graph is:

y < |x + 3|

Explanation:

By looking at the graph we see that the graph is a graph of a modulus function with vertex at (-3,0)

( The equation of modulus function with vertex at (-3,0) is given by:

y=|x+3| )

and the inequality must be strict since the line of the graph is dotted.

also, the shaded region is towards the origin.

Hence, the inequality must pass the zero point test.

Hence, the inequality which satisfies all these conditions is:

y < |x + 3|