contestada

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

Respuesta :

luisejr77

Answer:

Third option.

Step-by-step explanation:

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

If [tex]f(x)+k[/tex], the function is shifted down "k" units.

If [tex]f(x)-k[/tex], the function is shifted up "k" units.

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

If  [tex]-f(x)[/tex], the function is reflected over the x-axis.

Therefore, knowing that the parent function [tex]f(x) = log_3(x)[/tex]  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:

[tex]f(x) = -2log_3(x)-3[/tex]

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