what is the domain and range of `y=3e^(5x-6)`
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
The domain of a function y = f(x) is the set of values of x for which y is real and defined. The range of a function y = f(x) is the set of values of y for x lying in the domain.
For the function y = 3*e^(5x - 6), y is defined for all values of x. The domain of the function is the set of real numbers.
e is a positive number. It can therefore not take on any negative value or the value 0. This gives the range of the function as the set of positive real numbers.