Question

Does anyone know how to Graph f(x)=51(2)^x

Answer 1

F(x) = 102^x

Start with x=0.
f(0) = 102^(0) which is 1. Your y intercept (the line in the middle) is 0.

Your first point is (0,1).
For the second point, try x=1.

f(1) = 102^1 which is 102.
You second point is (1,102). Rinse and repeat. ;)

Answer 2

This is an exponential function.   

If x = 0, 2^x = 2^0 = 1.  The beginning value of 2^x is 1 and the beginning value of 51*2^x is 51.

Make a table and graph the points:

x        y=51*2^x                                point (x,y)
--       ---------------                            ---------------
0             51                                       (0,51)
2            51*2^2 = 51(4) = 204           (2,204)             and so on.

The graph shows up in both Quadrants I and II.  Its y-intercept is (0,51).  Its slope is always positive.