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Instructions: Determine whether graphs of each of the exponential functions would show vertical stretch or vertical compression and whether there is reflection over the x𝑥-axis.y=−2(3)x

Question

Instructions: Determine whether graphs of each of the exponential functions would show vertical stretch or vertical compression and whether there is reflection over the x𝑥-axis.y=−2(3)x

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Solution

The given function is y = -2(3)^x.

  1. Vertical Stretch or Compression: The coefficient of the function is -2. In general, if the absolute value of the coefficient is greater than 1, the graph of the function will show a vertical stretch. If the absolute value of the coefficient is less than 1, the graph will show a vertical compression. In this case, the absolute value of the coefficient is 2, which is greater than 1. Therefore, the graph of the function will show a vertical stretch.

  2. Reflection over the x-axis: The negative sign in front of the 2 indicates that there is a reflection over the x-axis. In general, if the coefficient of the function is negative, the graph of the function will be reflected over the x-axis. Therefore, the graph of the function y = -2(3)^x will be reflected over the x-axis.

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