How do you graph #y=2sqrt(x+2)# and compare it to the parent graph?

1 Answer
Sep 9, 2017

Determine and apply the transformations to the base function.


There are two transformations applied to this function.

Compared to the base function: #sqrtx#

graph{sqrtx [-10, 10, -5, 5]}

These transformations are:

  • Vertical stretch by a factor of #2#. This is caused by the #a#-value.
  • Horizontal translation #2# units to the left. Due to horizontal format of doing the opposite (essentially) of what would normally be done, the function moves.

As a result, we get a function that looks like this:

graph{2sqrt(x+2) [-10, 10, -5, 5]}

If we were to compare this to the parent graph, the transformed function is stretched and "starts" #2# units to the left.

Hope this helps :)