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 five units. which function is representative of this transformation?

a. g(x) = log3(2x) + 5
b. g(x) = log3(-2x) - 5
c. g(x) = -2log3(x) - 5
d. g(x) = 2log3(x) + 5

Answer 1

The The correct answer is option c. The function representative of the given transformations is g(x) = -2log3x - 5.

Step-by-step explanation:

The parent function f(x) = log3x has been transformed by reflecting it over the x-axis (which changes the sign of the function), stretching it vertically by a factor of two, and shifting it down five units. To represent these transformations in the function, we need to apply them in order:

1. Reflecting over the x-axis: change the sign of the function -> -f(x).

2. Stretching vertically by a factor of two: multiply the function by 2 -> -2f(x).

3. Shifting it down five units: subtract five from the function -> -2f(x) - 5.

Therefore, the function representative of this transformation is g(x) = -2log3x - 5, which corresponds to option c.