Question 314923
Break up the x-axis into a number of steps. 
How about 4 steps each 1 unit long. 
Start at x=-1.
Calculate y.
{{{x=-1}}},{{{y=2^(-1)=1/2}}}, (-1,1/2)
{{{x=0}}},{{{y=2^(0)=1}}}, (0,1)
{{{x=1}}},{{{y=2^(1)=2}}}, (1,2)
{{{x=2}}},{{{y=2^(2)=4}}}, (2,4)
{{{x=3}}},{{{y=2^(3)=8}}}, (3,8)
Plot those points.
{{{drawing(300,300,-4,4,-2,10,grid(1),
circle(-1,1/2, 0.2),
circle(0,1, 0.2),
circle(1,2, 0.2),
circle(2,4, 0.2),
circle(3,8, 0.2),
graph(300,300,-4,4,-2,10,0))}}}
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You can then connect the points with straight lines.
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{{{drawing(300,300,-4,4,-2,10,grid(1),
circle(-1,1/2, 0.2),
circle(0,1, 0.2),
circle(1,2, 0.2),
circle(2,4, 0.2),
circle(3,8, 0.2),
line(-1,1/2,0,1),
line(0,1,1,2),
line(1,2,2,4),
line(2,4,3,8),
graph(300,300,-4,4,-2,10,0))}}}
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Here is the graph of the actual function layed over the linear representation to show good a job the linear representation does.
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{{{drawing(300,300,-4,4,-2,10,grid(1),
circle(-1,1/2, 0.2),
circle(0,1, 0.2),
circle(1,2, 0.2),
circle(2,4, 0.2),
circle(3,8, 0.2),
line(-1,1/2,0,1),
line(0,1,1,2),
line(1,2,2,4),
line(2,4,3,8),
graph(300,300,-4,4,-2,10,2^x))}}}