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 xx or yy are zero. These give points on the two axis.
In function y=4^x-2y=4x−2, x=0x=0 gives y=-2y=−2 and y=0y=0 gives 4^x=24x=2 or x=log_(4)2=log2/log4=log2/2log2=1/2x=log42=log2log4=log22log2=12. Hence, two pints through which the curve passes are (0,-2)(0,−2) and (1/2,0)(12,0).
Further as xx appears as a power of 44 in y=4^x-2y=4x−2 as x->-oox→−∞ y=-2y=−2 hence we have a horizontal asymptote as y=-2y=−2.
We can also find a few other values, by putting xx as {-1,1,3/2,2,5/2,3}{−1,1,32,2,52,3} etc. We have use 22 in denominator as it is equivalent to square root of 44, easy to calculate. Values of xx are chosen narrowly spaced small values as too large values will lead to too large values of yy.
Using these values of xx, we get yy as {-7/4,2,6,14,30,62}{−74,2,6,14,30,62} and points are
(-1,-7/4)(−1,−74), (1,2)(1,2), (3/2,6)(32,6), (2,14)(2,14), (5/2,30)(52,30) and (3,62)(3,62). WE have already got (0,-2)(0,−2) and (1/2,0)(12,0). Further on left hand side the curve should tend to the value -2−2 as we have an asymptote.
Hence, the curve should be as shown below..
graph{y=4^x-2 [-10, 10, -5, 5]}
