Question

2. Which of the following inequalities would represent the graph shown?

f(x) ≤ √1-x
f(x) < √1-x
f(X) > √1-x
f(x) ≥ √1-x

Answer 1

`f(x) > √(1 -x)`

which is the third choice

Explanation:

We could just plot each and see which plot corresponds to the given graph

However, that is not necessary.

First note that the plot is a dotted line. This means the inequality is either a < inequality or a > inequality. If it were a ≤ or ≥ inequality, the plot of the line would be a solid line

That eliminates first and last choices

To see which of the remaining two options fits the graph, take a point in the shaded region and see which one satisfies which inequality .

Checking second choice....

Point (0, 2) is in the shaded region
Does (0, 2) satisfy the second choice:
`f(x) < √(1-x)\;\; ?`
Let's check by substituting 0 for the value of x

`1-x = 0\; so \; √(1-x) = √(0) = 0`

But the corresponding value of y should be 2, not 0 so this inequality is not satisfied for a point in the shaded region. Eliminate second choice

Third choice is the correct answer