Is there a some type of way in sketching y=2^x-2^-x , without using a table of values.

Answer 1

You just need a sense of basic graphs.
If you are dealing with these kind of graphs, you should have to know what
y = 2^x looks like.
for x>0 the y values will continue to increase as powers of 2

for x<0 the y values would simply be the negative of the y's obtained when x > 0 , so the graph increases sharply in the first quadrant and drops symmetrically in the third quadrant, making it look similar to y = x^3

Also when x = 0, it is easy to see that y = 0

You should be able to visualize what it looks like, if not, here is the graph:

https://www.wolframalpha.com/input/?i=Plot+y+%3D+2%5Ex+-+2%5E-x+from+-5+to+5