Question - Identifying Transformed Exponential Function
mathfunction transformationstransformed exponential functionvertical stretchreflection across x-axis
Solution:
The question asks which function g(x) represents the exponential function f(x) = 5^x after a vertical stretch by a factor of 2 and a reflection across the x-axis.Let's break down the transformations:1. Vertical stretch by a factor of 2: This means we multiply the original function f(x) by 2. So the function becomes 2 * 5^x.2. Reflection across the x-axis: To reflect a function across the x-axis, we take the negative of the function. So the function now becomes -2 * 5^x.Now, let's look at the answer choices and see which one matches our transformed function:A. g(x) = 2 * 5^(-x) - This represents a horizontal reflection across the y-axis instead of a vertical reflection and stretch. So, this is incorrect.B. g(x) = -2 * 5^(-x) - This represents a reflection across the x-axis and y-axis. So, this is incorrect.C. g(x) = 2 * 5^x - This represents a vertical stretch but no reflection across the x-axis. So, this is incorrect.D. g(x) = -2 * 5^x - This matches our description of a vertical stretch by a factor of 2 and a reflection across the x-axis.Therefore, the correct answer is D: g(x) = -2 * 5^x.
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