[Math] How to graph log equation if given the following

graphing-functionslogarithms

So the question is
$$ Y= log(-x+2)$$
So I factored as my teach told the class that $x$ can only be subtracted
so I factored out
$$ Y = log(-(x-2))$$
enter image description here

Information I got from the following equation
$$ a = 1$$ $$h= 2$$ $$k = 0 $$
$h = 2$ cause of the factored
so this is how I thought I would graph
enter image description here
if what was written in the picture wasn't clear because of resolution

Anchor point of the equation because 2 was $h$ so it has to move 2 units from the original $(3,0)$ is the anchor point. When I checked the answer I found out that I did it wrong as even if it reflected over $y$ axis, it would cross the asymtote

How would i do this?

Best Answer

No idea what's going on in the images but I'll go step by step as to how to graph the function.

  1. As you already got, from this you know two things: the asymptote is equal to 2 AND the equation is reflected along the y-axis\begin{equation} y = \log (-x+2) = \log(-(x-2))\end{equation}

  2. You find the anchor point by determining when y = 0, so \begin{equation} -x + 2 = 1 \end{equation}

    Therefore, x = 1.

  3. So to conclude, the graph should look like: http://i.imgur.com/wi6Bp0T.png?1

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