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

The graph of the parent function $y=\log x$ is well -known (see attached diagram for details, green curve).

Make such transformations:

1. translate graph of parent function $y=\log x$ 3 units to the left (violet curve), then you obtain the function  $y=\log (x+3);$
2. compress function $y=\log (x+3)$ in the x-direction by multiplying x by 3 (black curve), then you get the function $y=\log 3(x+3);$
3. reflect the function $y=\log 3(x+3)$ across the line $x=-3$ (red curve). You get the function $y=\log (-3(x+3));$
4. translate the function $y=\log (-3(x+3))$ 1 unit down (blue curve) to get the function $y=\log (-3(x+3))-1=\log (-3x-9)-1.$