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?

g(x) = log3(-2x) - 3
g(x) = log3(2x) + 3
g(x) = -2log3(x) - 3
g(x) = 2log3(x) + 3

Answer 1

Third option.

Explanation:

Some transformations for a function f(x), are:

If
`f(x)+k`, the function is shifted down "k" units.

If
`f(x)-k`, the function is shifted up "k" units.

If
`bf(x)`, and
`b>1`, the functio is stretch vertically by a factor of "b".

If
`-f(x)`, the function is reflected over the x-axis.

Therefore, knowing that the parent function
`f(x) = log_3(x)` was transformated by reflecting it over the x-axis, stretching vertically by a factor of 2 and shifting it down 3 units, we can determine that the following function represents the transformation:

`f(x) = -2log_3(x)-3`