Question

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 to x

For a point $(x, y)$ on $f(x)$, the x-coordinate for $g(x)$ is $x-1$ (shift left 1).

Step2: Apply vertical shift to y

The y-coordinate for $g(x)$ is $y-3$ (shift down 3).

Step3: Calculate first point

For $(0,0)$: $x' = 0-1 = -1$, $y' = 0-3 = -3$

Step4: Calculate second point

For $(1,1)$: $x' = 1-1 = 0$, $y' = 1-3 = -2$

Step5: Calculate third point

For $(9,3)$: $x' = 9-1 = 8$, $y' = 3-3 = 0$

Answer:

The point $(0, 0)$ on $f$ corresponds to $(-1, -3)$ on $g$.
The point $(1, 1)$ on $f$ corresponds to $(0, -2)$ on $g$.
The point $(9, 3)$ on $f$ corresponds to $(8, 0)$ on $g$.