The parent function f (x) = log5x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it down three units. Which function is representative of this transformation? g (x) = log5 (2x) - 3 g (x) = log5 (-2x) + 3 g (x) = - 2log5 (x) - 3 g (x) = 2log5 (x) + 3

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Asher Pearson

Mathematics

29 January, 18:24

The parent function f (x) = log5x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it down three units. Which function is representative of this transformation? g (x) = log5 (2x) - 3 g (x) = log5 (-2x) + 3 g (x) = - 2log5 (x) - 3 g (x) = 2log5 (x) + 3

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King Malone · Answer 1

To reflect it over the x axis, all y units get multiplied by - 1, so we multiply the equation by - 1. After that, to stretch it vertically, we multiply it by that factor, which is 2. Right now, we have - 2log (5x). Lastly, we shift it down 3 units by subtracting 3 from the overall equation, resulting in - 2log (5x) - 3