Question

The parent function f(x) = log3x 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?

Answer 1

`g(x)=-2log3x -3`

Explanation:

In order to stretch a function you need to multiply by a factor, in this case is two.

In order to shift your function vertically, you need to add or subtract a number, adding you shift up, subtracting you shift down. That's why wee subtract the 3 units, because it says 'shifting down'.

Answer 2

-2log3x - 3.

Explanation:

Reflecting over the x axis gives - log 3x.

A vertical stretch gives the function -2log3x.

Finally a shift down 4 units gives the function -2log3x - 3.