Example Question - exponential function transformation

Transformation of Exponential Function

To solve this problem, we'll consider the transformations required step by step. The given function is f(x) = 5^x, and we are asked to apply the following transformations: 1. Vertical stretch by a factor of 2. 2. Reflection across the x-axis. 1. A vertical stretch by a factor of 2 will multiply the function by 2. This does not affect the exponent, so the new function after this transformation will be: h(x) = 2 * f(x) = 2 * 5^x 2. A reflection across the x-axis means we need to take the negative of the function. So the final function after this reflection will be: g(x) = -h(x) = -2 * 5^x This matches option B: g(x) = -2(5^x).