Question

Write an equation for the graphed function by using transformations of the graphs of one of the toolkit functions.

Answer 1

`y=√(x+3)-1`

Explanation:

This is the curve of
`y=√(x)` with some transformations applied.

The curve appears to be moved left 3 units and down 1 unit.

The pictured curve is that of
`y=√(x-(-3))-1` or after simplifying
`y=√(x+3)-1`.

Check it!

Plug in some points on the given curve into the equation we said that fits it.

Here are some points I see on the curve:

(-3,-1)

(-2,0)

(1,1)

Let's see if those points satisfy our equation.

`y=√(x+3)-1` with
`(x,y)=(-3,-1)`:

`-1=√(-3+3)-1`

`-1=√(0)-1`

`-1=0-1`

`-1=-1` is true so (-3,-1) does satisfy
`y=√(x+3)-1`.

`y=√(x+3)-1` with
`(x,y)=(-2,0)`:

`0=√(-2+3)-1`

`0=√(1)-1`

`0=1-1`

`0=0` is true so (-2,0) does satisfy
`y=√(x+3)-1`.

`y=√(x+3)-1` with
`(x,y)=(1,1)`:

`1=√(1+3)-1`

`1=√(4)-1`

`1=2-1`

`1=1` is true so (1,1) does satisfy
`y=√(x+3)-1`.

All three points that crossed nicely fit the equation we described.