Graph of $\log_2(2-x)$: what is wrong in my transformational approach?

Question

In the graph of $\log_2(2-x)$ can I have the transformational approach of $\log_2 x$ >> $\log_2(-x)$ >> $\log_2(-x+2)$ or $\log_2(2-x)$ but after all this graph comes wrong but with differential approach graph comes right. What is wrong in my graph transformational approach?

Answer 1

When you perform the transformation $\log_{2}(-x)>>\log_{2}(-x+2)$, you want to write $\log_{2}(-x+2)$ as $\log_{2}(-(x-2))$, since this shows that you are shifting the graph of $y=\log_{2}(-x)$ two units to the right.

Answer 2

It might be more clear to do the shift before the reflection: $$\log_2(x)\to\log_2(x+2)\to\log_2(-x+2)$$ Speaking loosely, you enacted the horizontal shift with a ${}+2$ right on inside the function input parentheses. But a horizontal transformation should be enacted upon the input variable. And if you had already done the reflection, there is a layer of minus sign between the input variable and the function input parentheses.