Use transformations to graph the following function. Also state (a) the domain, (b) the range, (c) the horizontal asymptote. f(x)= 3^(x+2)
You need to select the base function the exponential function `f(x) = 3^x` . The function `f(x)=3^(x+2)` is the result of transformations occured in `f(x)=3^x` .
If you substitute x + 2 for x, then the graph of function `f(x) = 3^x` is translated to the left by 2 units.
Sketching the graphs of the base function and the transformed function yields:
Notice that the black curve representing the function `y=3^x` moves to the left by 2 units. The red curve represents the graph of transformed function `y = 3^(x+2).`
The domain of the exponential function `3^(x+2)` is f(x)= the real set and the range is the set `(0,oo).` Notice that exponential function has no vertical asymptote but the negative x axis represents the horizontal asymptote.