# How do you graph y=log_5(2x+2)+5?

Nov 25, 2017

It is the graph of $y = {\log}_{5} x$ with a horizontal translation of 1 unit left, horizontal compression of $\frac{1}{2}$, and a vertical translation of 5 units up!

#### Explanation:

To graph $y = {\log}_{5} x$, you can change it to an exponential equation, which would be ${5}^{y} = x$ and pick some values of y to find x values.
This would give you the 'original' graph.

$y = \setminus {\log}_{5} \setminus \left(2 x + 2\right) + 5$ could be changed to $y = \setminus {\log}_{5} \setminus 2 \left(x + 1\right) + 5$

From that graph, the transformed values are:
--> K = $- 1$, which means that the graph of $y = {\log}_{5} x$ is horizontally translated 1 unit left.
--> D = 2, which means that $y = {\log}_{5} x$ is horizontally compressed by a factor of $\frac{1}{2}$.
--> H = 5 which means that $y = {\log}_{5} x$ is vertically translated 5 units up.

Also note that due to these transformations, the vertical asymptote is translated 1 unit left, to $x = - 1$.