Question

Of the following, which best represents the graph of the region that corresponds to the inequalities 0 ≤ y ≤ 3 and x ≥ 0?

Is it Option 1 (all the way at the top), Option 2 (in the middle), or Option 3 (on the bottom)?
Or is it neither of them at all?

Answer 1

Option 1 is the correct answer.

Let's look at our constraint for the y value:

`0\leq y\leq 3`. Remember that these are greater/lesser than or equal to symbols.

You can tell which way they're facing by what direction they open up in.
In this case, the first opens towards y, and the second opens towards 3.
This means that y is greater than or equal to 0, but lesser than or equal to 3.

This means that y, the vertical axis, can go from anywhere to 0 to 3.
Let's look at the constraint for the x value:

It's
`x\geq 0`. The sign is facing towards x, which means that x is greater than or equal to 0.

This means x (the horizontal axis) can range from 0 to positive infinity.

The y axis will not go above 3, and will not go below 0.
The x axis will not go below 0.

The only graph that satisfies these conditions is Option 1.

The y value does not go past 3, and does not go under 0.

The x value does not go to the left of 0, but goes on forever to the right.