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I think the correct answer from the list of choices above is the second option. However, the second choice should contain the exponent sign(^). The correct function should be  f(x) = 3^(x + 3). The graph given shows an exponential growth so the equation should as well be an exponential one.

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using a graph tool

I proceed to graph each case to determine the solution


case A) \(f(x)=3^{x}-3\)

see the attached figure N 1------> is not the solution


case B) \(f(x)=3^{(x+3)}\)

see the attached figure N 2--------> is the solution


case C) \(f(x)=3^{x}\)

see the attached figure N 3-----> is not the solution


case D) \(f(x)=3^{x}+3\)

see the attached figure N 4-----> is not the solution


therefore


the answer is the option

case B) \(f(x)=3^{(x+3)}\)

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