Johnston Wells
07/24/2023 · Junior High School
Solve the following problems. Write step by step solutions and justify your answers. Work Problem 1 . (a) ( 15 Points) Graph the function \( f(x)=-2 e^{2 x+4}+7 \), not by plotting points, but by starting the graph of one of the standard functions and applying an appropriate transformation.
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To graph \( f(x) = -2 e^{2x + 4} + 7 \), start with \( g(x) = e^x \), apply a horizontal compression by a factor of \( \frac{1}{2} \), shift left by 2 units, reflect across the x-axis, stretch vertically by a factor of 2, and finally shift up by 7 units. The key point to plot is \( (-2, 5) \).
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