Begin by graphing $$ f(x)=2^{x} $$. Then use transformations of this graph to graph the given function. Be stre to graph and give the eqpation your hand drawn graphs. $$ h(x)=2^{x+2}+2 $$ Which transformations are needed to graph the function $$ h(x)=2^{x+2}+2 $$ ? Choose the correct answer below. A. The graph of $$ f(x)=2^{x} $$ should be horizontally shifted 2 units to the left and vertically shiffed 2 units upward. B. The graph of $$ f(x)=2^{x} $$ should be horizontally shifted 2 units to the left and vertically shifted 2 units downward. C. The graph of $$ f(x)=2^{x} $$ should be horizontally shifted 2 units to the right and vertically shifted 2 units downward. D. The graph of $$ f(x)=2^{x} $$ should be horizontally shifted 2 units to the right and verticalty shifted 2 units upward

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1. Begin with the graph of $$\, f(x)=2^{x} $$. This is an exponential curve that passes through the point $$(0,1)$$, has a horizontal asymptote on the $$x$$-axis, and increases as $$x$$ increases.

2. Consider the function $$\, h(x)=2^{x+2}+2$$.

3. Notice that the function can be seen as applying two transformations to $$f(x)$$:
   - The term $$\, x+2 $$ inside the exponent indicates a horizontal shift. Since the term is $$x+2$$, the graph shifts 2 units to the left.
   - The $$+2$$ outside the exponential function indicates a vertical shift. The graph moves 2 units upward.

4. Therefore, the graph of $$ f(x)=2^{x} $$ is **horizontally shifted 2 units to the left** and **vertically shifted 2 units upward** to obtain the graph of $$ h(x)=2^{x+2}+2 $$.

5. The correct choice is:

A. The graph of $$\, f(x)=2^{x} $$ should be horizontally shifted 2 units to the left and vertically shifted 2 units upward.
To graph $$ h(x)=2^{x+2}+2 $$, shift the graph of $$ f(x)=2^{x} $$ 2 units to the left and 2 units upward.

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