graph the exponential function of y=1.5^x over the domain {x: -7 <x< 7}

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graph the exponential function of y=1.5^x over the domain {x: -7 <x< 7}

 

Note that exponential functions are of the form `y=ab^x` . If the coefficient a<0 the exponential is reflected over the x-axis. The |a| determines the "steepness" of the function -- a acts as a vertical stretcher or compressor. Here a=1 so there are no major changes.

If 0<b<1 then this would be an exponential decrease; since b>1 we have an exponential increase.

Now we can create a table of values to find points on the curve: `(x,y)->(x,(3/2)^x)` . Thus we get (-2,4/9),(-1,2/3),(0,1),(1,3/2),(2,(9/4). Plotting these and connecting with a smooth curve we get:

as required.

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