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How do you graph #y=(1/2)^x# using a table of values?

Answer 1

Take some #(x,y)# samples and connect them.

Unfortunately, we can draw exact graph of very few functions. Table of values can help drawing every (other) function, but you will never reach #100%# accuracy, since you can't tell what happens in the middle of your samples.

Anyway, it's pretty straightforward: you just choose a bunch of #x# values, and compute their images #y#, using the rule described by the function.

In your case, we may restyle the function a little bit by writing

#(1/2)^x = 1/2^x#

and thus, for example, if we choose the #x# values #-3,-2,-1,0,1,2,3# we have corresponding values

#-3\to1/2^(-3)=8# #-2\to1/2^(-2)=4# #-1\to1/2^(-1)=2# #0\to1/2^0=1/1=1# #1\to1/2^1=1/2# #2\to1/2^2=1/4# #3\to1/2^3=1/8#

Plot all the #(x,y)# couples you got and try to sketch the rest of the function accordingly

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Answer 2

Jameson Allen

x	y
-2	4
-1	2
0	1
1	0.5
2	0.25

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.