y=f(x-4)+1


use the graph of y=f(x) shown to skech the graph of the given function
( given graph pionts are -2,3 1,2 and 2,0

the graph of y = f(x) moves 4 units to the right, and one unit up

points are written with brackets,
I will assume your points are (-2,3), (1,2) and (2.0)

so

(-2,3) -----> (2,4)
(1,2) ------> (5,3)
(2,0) ------> (6,1)

To sketch the graph of the given function y = f(x-4) + 1 using the given points (-2,3), (1,2), and (2,0) on the graph of y=f(x), you can follow these steps:

1. Start by locating the given points on the graph of y=f(x). Plot the points (-2,3), (1,2), and (2,0) on the graph. These points might not be explicitly labeled on the graph but use the given coordinates to approximate their positions.

2. Since the given function is y = f(x-4) + 1, each x-coordinate of the original graph needs to be shifted 4 units to the right. Therefore, for each x-coordinate on the graph, add 4 to it.

- The point (-2,3) on the original graph will now be located at (-2+4, 3) = (2, 3).
- The point (1,2) on the original graph will now be located at (1+4, 2) = (5, 2).
- The point (2,0) on the original graph will now be located at (2+4, 0) = (6, 0).

3. Finally, since the given function is y = f(x-4) + 1, there is also a vertical shift upward by 1 unit. Therefore, for each y-coordinate on the graph, add 1 to it.

- The point (2,3) will now be shifted upward to (2, 3+1) = (2, 4).
- The point (5,2) will now be shifted upward to (5, 2+1) = (5, 3).
- The point (6,0) will now be shifted upward to (6, 0+1) = (6, 1).

4. Connect the transformed points (2,4), (5,3), and (6,1) with a smooth curve. This curve will represent the graph of the given function y=f(x-4)+1, based on the original graph of y=f(x).

Note: If there are other points on the original graph that are not given, you can also transform those points using the same steps mentioned above to obtain additional points to sketch the graph.

To sketch the graph of the function y = f(x-4) + 1 using the given graph points (-2,3), (1,2), and (2,0), you will need to shift the graph of f(x) four units to the right and one unit up.

Here are the steps to sketch the graph:

1. Start with the original graph of y = f(x). Note the shape and position of the graph.
2. Shift the graph four units to the right. This means that every x-coordinate of the points on the graph should be increased by 4. For example, the point (-2,3) would become (2,3).
3. Shift the graph one unit upward. Add 1 to the y-coordinate of each point on the graph. For example, the point (2,3) would become (2,4).
4. Plot the new points obtained from the shifts: (2,4), (5,3), and (6,1).
5. Connect the plotted points to sketch the graph of y = f(x-4) + 1.

Remember that without the information about the shape and position of the graph of f(x), the sketch will only be an approximation based on the given points and the general idea of the shifts.