How do you describe the transformation of #f(x)=sqrt(x+4)+8# from a common function that occurs and sketch the graph?
1 Answer
The 8 shifts the graph up 8 and the 4 shifts the graph left 4.
Explanation:
The parent function is:
There is a number inside the square root and a number outside the square root that is being added to this function.
The number on the inside always shifts it in the x direction. If the number is positive, it shifts the graph to the left and if the number is negative, it shifts the graph to the right.
Since our number is a positive 4, it will shift our graph to the left 4 spaces.
The number being added will always shift it in the y direction. If the number is positive, it shifts the graph up and if the number is negative, it shifts the graph down.
Since our number is a positive 8, it will shift our graph up 8 spaces.
When graphing it, our curve takes on a square root shape since our parent function is a square root function:
graph{sqrt(x+4)+8 [-8.4, 14.11, 5.025, 16.265]}
