Question

In two or more complete sentences, describe the transformation(s) that take place on the parent function,

f(x) = log(x), to achieve the graph of g(x) = log(-3x - 9) - 1.

Answer 1

`log( - 3x - 9) = log( 3( - x - 3)) \\ = log( 3) + log( - (x + 3))`

A vertical shift by 1 unit downwards

A vertical shift by log(3) units upwards

A horizontal shift by 3 units to the left

A reflection along the line x=-3

Answer 2

The function g(x) = log(-3x - 9) - 1 is obtained from the parent function f(x) = log(x) through two transformations: a shift to the right and a shift downward. The shift to the right is achieved by multiplying x by -3 and subtracting 9, which results in a rightward shift in the function's graph. The shift downward is achieved by subtracting 1 from the final result, which results in a downward shift in the function's graph. These transformations result in a graph that is shifted to the right and downward compared to the graph of the parent function.