what is the domain and range of `y=3e^(5x-6)`

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The domain of `5x-6` is, since this is a linear function, set of all real numbers. Domain of exponential function `e^x` is also set of all real numbers so the domain of your function `y=3e^(5x+6)` is set of all real numbers `RR.`  

Range of linear function `5x-6` is set of all real numbers, but range of exponential function `3e^x` is set of all positive numbers `(0,+oo).` Hence the range of composition of those two functions,that is of your function `y=3e^(5x-6)` is set of all positive numbers `(0,oo).`  

Graph of the function

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