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

1 Answer
Noah G
Aug 27, 2017

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:

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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.

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Hopefully this helps!

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