Answer: Last Option
[tex]y> | x + 1 | +3[/tex]
Step-by-step explanation:
First we must identify the function shown in the graph.
It is a function of absolute value whose vertex is in the point (-1, 3)
The absolute value parent function is:
[tex]h(x) = | x |[/tex]. And it has its vertex in (0, 0)
The function shown in the graph is the function h(x) displaced 1 unit to the left and 3 units to the top.
Therefore the function shown in the graph [tex]f(x) = h (x + 1) +3[/tex]
[tex]f (x) = | x + 1 | +3[/tex].
Then, the region shaded in the graph are all the values of y that are above the graph of [tex]f (x) = | x + 1 | +3[/tex]
That is, the region is formed by all values where y is greater than [tex]f (x) = | x + 1 | +3[/tex]
Then the inequality is:
[tex]y> | x + 1 | +3[/tex]
