Question

the parent function for $g(x)=\sqrt{x + 2}-4$ is $f(x)=\sqrt{x}$.
part 2 of 4
the graph of $g$ is the graph of $f$ shifted 2 units to the left and 4 units downward.
part: 2 / 4
part 3 of 4
we can plot several \strategic\ points as an outline for the new curve.
the point $(0, 0)$ on the graph of $f$ corresponds to $(\square, \square)$ on the graph of $g$.
the point $(1, 1)$ on the graph of $f$ corresponds to $(\square, \square)$ on the graph of $g$.
the point $(9, 3)$ on the graph of $f$ corresponds to $(\square, \square)$ on the graph of $g$.

Explanation:

Step1: Apply horizontal shift left 2

For a point $(x,y)$ on $f(x)$, the $x$-coordinate of the corresponding point on $g(x)$ is $x-2$.

Step2: Apply vertical shift down 4

For a point $(x,y)$ on $f(x)$, the $y$-coordinate of the corresponding point on $g(x)$ is $y-4$.

Step3: Calculate point (0,0) mapping

New $x$: $0 - 2 = -2$; New $y$: $0 - 4 = -4$

Step4: Calculate point (1,1) mapping

New $x$: $1 - 2 = -1$; New $y$: $1 - 4 = -3$

Step5: Calculate point (9,3) mapping

New $x$: $9 - 2 = 7$; New $y$: $3 - 4 = -1$

Answer:

The point $(0, 0)$ on $f$ corresponds to $(-2, -4)$ on $g$.
The point $(1, 1)$ on $f$ corresponds to $(-1, -3)$ on $g$.
The point $(9, 3)$ on $f$ corresponds to $(7, -1)$ on $g$.