Question

Describe how to translate the graph of y=√x to obtain the graph of y=√x-13

A: Shift down 13 units
B: Shift right 13 units
C: Shift left 13 units
D: Shift up 13 units

Answer 1

A: Shift down 13 units

Answer 2

A: Shift down 13 units

Explanation:

Vertical and horizontal translations are displacements of a function in the coordinate system (x, y). If we translate the graphical representation of a given function, we will obtain representations of related functions. If we perform a vertical translation of a function, the graph will move from one point to another certain point in the direction of the "y" axis, that is, up or down. On the other hand if we perform a horizontal translation of a function, the graph will move from one point to another determined point in the direction of the "x" axis, that is, to the right or to the left.

If you want to do a vertical translation, let:

`k>0\\\\k\in R`

Then:

`y=f(x)+k` : Shifts the graph
`k` units up.

`y=f(x)-k`: Shifts the graph
`k` units down.

If you want to do a horizontal translation, let:

`h>0\\\\h\in R`

Then:

`y=f(x+h)` :Shifts the graph h units to the right.

`y=f(x-h)`: Shifts the graph h units to the left.

In this sense, if you want to obtain the graph
`y=√(x) -13` from the graph
`y=√(x)` basically you need to shift the graph
`y=√(x)` 13 units down:

`y=(√(x) )-13=√(x) -13`

I attached you the graphs.