College Algebra

Question

The graph of the parent function   has been shifted both horizontally and vertically. Give the equation of the translated graph pictured below.

Answer 1

I wasn't able to see your pictures, however, perhaps I can explain the effects of horizontal and vertical shifts.

The parent function is y=√x. Transformations from the parent function is in are in the form of y=√(x-h)+k, where h is the horizontal translation and k is the vertical translation.

If perhaps, you were given a graph that is clearly translated two units right and 5 units down, then the equation of the function would be y=√(x-2)-5. Be careful with the sign in the square root. The root can never be negative. This affects the shift of the function left/right:

Example: Describe the transformation of y=√(x-4)+2

Answer: Right 4, up 2

Example: Describe the transformation of y=√(x+4)+2

Answer: Left 4, up 2

As you can see, the sign in the radical, if negative, shifts the function right and vice versa. For the vertical shift "k", this is on the outside of the function, so if k is positive then it moves up and if negative, moves down.