To graph any function, we should have a broad idea about the function. As far as possible choose points carefully. Initially it makes good sense to pick up points where x or y are zero. These give points on the two axis.
In function y=4x−2, x=0 gives y=−2 and y=0 gives 4x=2 or x=log42=log2log4=log22log2=12. Hence, two pints through which the curve passes are (0,−2) and (12,0).
Further as x appears as a power of 4 in y=4x−2 as x→−∞ y=−2 hence we have a horizontal asymptote as y=−2.
We can also find a few other values, by putting x as {−1,1,32,2,52,3} etc. We have use 2 in denominator as it is equivalent to square root of 4, easy to calculate. Values of x are chosen narrowly spaced small values as too large values will lead to too large values of y.
Using these values of x, we get y as {−74,2,6,14,30,62} and points are
(−1,−74), (1,2), (32,6), (2,14), (52,30) and (3,62). WE have already got (0,−2) and (12,0). Further on left hand side the curve should tend to the value −2 as we have an asymptote.
Hence, the curve should be as shown below..
graph{y=4^x-2 [-10, 10, -5, 5]}
