Question

Sketch the graph `{(x,y)|(y<=2^x)nn(y>=0)nn(x>=-2)}` ?

Answer 1

I like to go step by step in these problems. We start by sketching the graph of `y ≤ 2^x`.

This is an exponential function of base `2`, so it's going to increase rather quickly. It should be drawn with a solid line because the inequality is `≤` instead of `<`. The graph of `y = 2^x` should look like this:

We now shade under the curve `y = 2^x`, but only where `x ≥ -2` and `y ≥ 0`. The solution region will be of the following shape. But beware that when you are tracing your graph, you have to continue the graph towards negative `-oo` without shading.

Hopefully this helps!