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 up three units. Which function is representative of this transformation?

The function formed is g (x) - 2log5x+3 ...

Step-by-step explanation:

According to the given statement 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 up three units.

We have to find which function is representative of this transformation?

Solution:

The parent function y = log5x has been transformed by reflecting it over the x-axis.

f (x, y) ⇒f (x,-y)

-y = log5x

y = - log5x

Now stretching it vertically by a factor of two means multiply the factor by output constant given.

y = - 2log5x

Then shifting it up three units:

It means f (x) ⇒f (x) + b function shift upwards by b units.

y = - 2log5x+3

Thus the function formed is g (x) - 2log5x+3 ...