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

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

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Answer 1 · 2017-08-27T15:54:20

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:

enter image source here

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.

enter image source here

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

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