What does this mean?

Question

Write an equation for a function that has a graph with the given characteristics.

The shape of  shifted left 6 units and shifted up 3 units.

Answer 1

Answer 2

When the graph of a function is "shifted" to the "left" or to the "right", it is a move along the axis "x" and it will have something to do with changes in argument "x".

When the graph of a function is "shifted" "up" or "down", it is a move along axis "y" and it will have something to do with changes in a function itself.

Original function: y = 5√x

Function shifted 6 units to left: y = 5√(x + 6) ← x- coordinate of each point of the function became 6 units smaller

Function shifted 6 units to left and 3 units up: y = 5√(x + 6) + 3 ← in addition to changes in "x" in previous transformation, y-coordinate of each point of the function became 3 units larger

Note that "unit" is the scale of the graph.