Summarize the pertinont information obtained by applying the graptung stratogy and skotch the graph of \( \mathrm{y}=\mathrm{I}(\mathrm{x}) \). \( f(\mathrm{x})=e^{0.3 x}+256 \mathrm{e}^{-0.5 \mathrm{x}} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of I is (Type your answer in interval notation. Use a comma lo separate answers as needed.) B. The domain of I is empty.
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The function \( f(x) = e^{0.3x} + 256e^{-0.5x} \) is defined for all real numbers, as both components \( e^{0.3x} \) and \( 256e^{-0.5x} \) can be calculated for any value of \( x \). Therefore, the domain of \( f(x) \) is \( (-\infty, \infty) \). In terms of graphing, the function \( f(x) \) tends to grow exponentially for large positive \( x \) due to the \( e^{0.3x} \) term, while for large negative \( x \), the term \( 256e^{-0.5x} \) dominates and provides a positive output, keeping the function above zero and giving it an interesting shape with a steep rise.
