graph the points for f(x) =2(1/2)^x+1

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steveschoen | College Teacher | (Level 1) Associate Educator

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First thing to consider is recognizing that this is an exponential function.  Thus, it is going to look something like either the red or black line in the first attachment I put here.

Then, recalling the base/parent function for exponential functions has the x axis ("y = 0") an as asymptote.  But, there, the "+ 1" is going to move the entire plot up 1.  So, the asymptote because "y = 1".

Then, finally, for exponentials, some teachers may differ on how many points to plot.  I have my class graph 3 points.  You literally pick numbers for x, then plug them into the function to see what f(x) becomes.  I picked -1, 0, and 1 for x, as my table shows in the graph attachment.  I got f(x) being 5, 3, and 2, respectively.  Then, you plot the points and connect the dots, being careful to maintain the curve for an exponential function and that the graph doesn't cross "y = 1".

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