Question

I need help wit 7&8 they are one whole question

Answer 1

Notice that the graph of f(x) includes the point (10,1), after applying each listed transformation to (10,1), we get

`\begin{gathered} (10,1)\rightarrow(10-2,1)=(8,1)\rightarrow\text{ 2 units to the left} \\ (10,1)\rightarrow(10-10,1)=(0,1)\rightarrow10\text{ units to the left} \\ (10,1)\rightarrow(10,-1)\rightarrow\text{ reflection over the x-axis} \\ (10,1)\rightarrow(-10,1)\rightarrow\text{ reflection over the y-axis} \\ \end{gathered}`

Thus, g(x) is a reflection across the y-axis of f(x).

The answer to 7) is option D.

8)

In general, a reflection across the y-axis is given by the transformation below

`(x,y)\rightarrow(-x,y)`

Therefore, in our case,

`g(x)=f(-x)=log(-x)`

The answer is g(x)=log(-x), option C.