# describe how the graph of y = 3^x + 2 is related to the graph of its parent function

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Given a function f(x), a transformation of the graph of the function given by g(x)=af(x-h)+k can be described by:

a: is a vertical stretch/compression of factor a

h: is a horizontal translation (slide) of h units

k: is a vertical translation of k units.

So for `y=3^x+2` we have the parent function `y=3^x` , and the transformation is a translation of 2 units up.

The graph of `y=3^x` in black; the transformation in red:

Notice that for each x, the y value of the transformed graph is 2 more than the parent graph.

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If instead you had `y=3^(x+2)` then the transformation would be a horizontal shift left of two units.

first we have to see that the funcion `y=3^x+2` si the function

`y=3^x` as parallel lines.

so that have the same field of definition, `(-oo;oo)`

(balck line `y=3^x+2` red line `y=3^x` )

and the same derivative: `y'= 3^(x)ln3`

Let you see we have added previous graph derivative funtion(blue line)