Question

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

y ≥ x + 1
y ≥ |x| + 1
y ≥ |x - 1|

Answer 1

y≥|x-1|
The lines represented are the line y=x-1 and the line y=x-1 itself in the positive section of the graph (absolute value).

Answer 2

The correct option is C)
`y\geq |x+1|`

Explanation:

The graph of
`y=|x|` is shown in figure-1

In option (1)
`y\geq x+1` .....(2)

the graph of equation (2) is shown in figure-2

In option (2)
`y\geq |x|+1` .....(3)

the graph of equation (3) is shown in figure-3

In option (3)
`y\geq |x+1|` .....(4)

the graph of equation (3) is shown in figure-4

As this is shifted 1 unit to right side

So, this figure is correct as it is matches the provided figure

Therefore, the correct option is C)
`y\geq |x+1|`