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Let's analyze each

The atmospheric pressure is lower at 15 miles above sea level than at 10 miles above sea level.  --> true

In fact, we see that the pressure at 15 miles above sea level is less than 1 pound per square inch, while the pressure at 10 miles above sea level is almost 2 pound per square inch.

As the altitude increases, the atmospheric pressure increases.  --> false

It's actually the opposite: from the graph, we see that as the altitude increases (going towards right on the graph), the pressure decreases.

The atmospheric pressure is 14 pounds per square inch at sea level.  --> true

If we take altitude=0, we see that the value of the pressure is 14 pounds per square inch.

As the altitude approaches sea level, the atmospheric pressure increases.  --> true

As the altitude approaches sea level (so, going towards left in the graph), we see that the value of the pressure increases.

The atmospheric pressure gets close to 14 pounds per square foot as the altitude continues to increase. --> false

The pressure is 14 pounds per square inch only when the altitude is 0 miles above sea level.