SOLUTION: Sketch the graph of each function. state the domain and range, and whether the function is increasing or decreasing. identify any aysmptotes. f(x)=2^x-3

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i am assuming the equation is y+=+2%5E%28x-3%29

and not

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%28300%2C+200%2C+-3%2C+5%2C+-1%2C+6%2C+2%5E%28x-3%29%29

graph%28300%2C+200%2C+-3%2C+5%2C+-1%2C+6%2C+2%5E%28x-3%29%29

.
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.