Use transformations to graph the following function. Also state (a) the domain, (b) the range, (c) the horizontal asymptote. f(x)= 3^(x+2)

Asked on by solo123456

sciencesolve | Teacher | (Level 3) Educator Emeritus

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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.

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