How do you describe the transformations from the parent graph of (x) = Sqrt(x)

How do you describe the transformations from the parent graph of (x) = Sqrt(x) When the problem is g(x) = -1/2 sqrt(1/5(x+5))+7

I always find these fascinating - lets look at the 2 graphs

Now I think I will look at it one step at a time.

(x) = Sqrt(x) When the problem is g(x) = -1/2 sqrt(1/5(x+5))+7

$$\\f(x) = \sqrt{x} \\\\
$First move the graph 5 places to the LEFT$\\\\
f_2(x) = \sqrt{x+5} \\\\
$now multiply all the y values by a factor of $ \frac{1}{2\sqrt{5}}\\\\
f_3(x) =\frac{1}{2\sqrt{5}} \sqrt{x+5} \\\\
$now simplify$\\\\
f_3(x) = \frac{1}{2 }\sqrt{\frac{x+5}{5}}\\\\
$now reflect the graph in the y axis (mult by -1)$\\\\
f_4(x) = \frac{-1}{2 }\sqrt{\frac{x+5}{5}}\\\\
$Now raise the graph by 7 units$\\\\
g(x) = \frac{-1}{2 }\sqrt{\frac{x+5}{5}}+7$$

I have done this transformation - bit by bit - in Desmos

https://www.desmos.com/calculator/k9mcqmsbq9

you can click on the coloured circles on the left to display or hide each graph

Start with only the top graph displayed.

Then reveal each next graph one at a time.  That way you will see how the transformation takes place.

It is really COOL !!

Thanks for this, Melody.....I want to look at this one a little more....

Hi Chris,

If I have to graph by hand this is the way I always do - as a build up from a parent graph.

I am still not as good at it as I would like to be but thinking about what should happen and then testing it with Desmos graphing calculator is an easy, efficient way to practice and to check one's logic.