Question

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

Answer 1

Answer:

f(x) = -3log5x -3

Step-by-step explanation:

Please see a logarithmic function after translation can be given by :

f(x)=alog(x-h)+k

here h is horizontal shift

k is vertical shift and a is stretch or compress

and for reflection over x-axis we just multiply by -1

so using all this information , we know that we have to reflect it over x axis and horizontal shift is 0 and vertical shift is 3 units down that means -3

so plugging in all the values in the standard form , we get

f(x)=-3log(5(x-0))-3

This can be simplified further as:

f(x)=-3log(5x)-3

That's the final answer

Hope it was helpful