Question 1787
i am assuming the equation is {{{y = 2^(x-3)}}} and not {{{y = (2^x)-3}}}

so, it is a log graph...you should learn how a log or exponential graph looks.

Always look for "obvious" points on any sketching...usually where x=0 and where y=0, although in exponentials, it is better to find where y=1 usually.

so, if x=0, then y=1/8.
if y=1, then x=3.

the curve never quite reaches the x-axis on the -ve x-side...put in a large -ve x-value and you will see this.

{{{graph(300, 200, -3, 5, -1, 6, 2^(x-3))}}}.

the graph is increasing and has an asymptote at x=0, as the function 


sorry, i missed off the domain and range...

domain is xeR (ie all real values of x)
range is yeR, y>0 (ie all real values greater than 0, since no -ve y values are possible...nor is zero).


cheers
Jon.