Question

Choose the inequality whose graph is shown.

Answer 1

Option c

`y\leq -√(x) +1`

Explanation:

To solve this type of problem the most efficient method is to select any point within the shaded region, for example, point (1,-1). Then introduce this point in the inequality:

`y\leq -√(x) +1`

Then we have left:

`(-1)\leq -√(1) + 1`

Note that the inequality is satisfied.
`- √(1) +1 = 0` is greater than -1

Now we take the inequality shown in option c
`y\leq -√(x) +1` and substitute a point belonging to the curve
`y = -\sqrt {x} +1`

This point is (1, 0)

`(0) \leq -√(1) +1`

`(0) \leq 0`

Note that the inequality is satisfied. Therefore the correct option is the option c