Question

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

Answer 1

Answer:

$y=\sqrt{x+3}-1$

Step-by-step explanation:

This is the curve of $y=\sqrt{x}$ with some transformations applied.

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

The pictured curve is that of $y=\sqrt{x-(-3)}-1$ or after simplifying $y=\sqrt{x+3}-1$.

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.

$y=\sqrt{x+3}-1$ with $(x,y)=(-3,-1)$:

$-1=\sqrt{-3+3}-1$

$-1=\sqrt{0}-1$

$-1=0-1$

$-1=-1$ is true so (-3,-1) does satisfy $y=\sqrt{x+3}-1$.

$y=\sqrt{x+3}-1$ with $(x,y)=(-2,0)$:

$0=\sqrt{-2+3}-1$

$0=\sqrt{1}-1$

$0=1-1$

$0=0$ is true so (-2,0) does satisfy $y=\sqrt{x+3}-1$.

$y=\sqrt{x+3}-1$ with $(x,y)=(1,1)$:

$1=\sqrt{1+3}-1$

$1=\sqrt{4}-1$

$1=2-1$

$1=1$ is true so (1,1) does satisfy $y=\sqrt{x+3}-1$.

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