Question

How do you describe the transformation of `f(x)=sqrt(x+4)+8` from a common function that occurs and sketch the graph?

Answer 1

The 8 shifts the graph up 8 and the 4 shifts the graph left 4.

Explanation:

The parent function is:

`f(x)=sqrtx`

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]}