Answer:

Whatever your function f(x)f(x) is, will undergo the following transformations sequentially :

1. f(x)→f(x−1)f(x)→f(x−1) : Graph shifts laterally by 1 unit towards positive x-axis.

2. f(x−1)→−f(x−1)f(x−1)→−f(x−1) : Graph is inverted about the x-axis (made to rotate by 180°).

3. −f(x−1)→−f(x−1)+1−f(x−1)→−f(x−1)+1: Graph shifts by 1 unit towards positive y-axis.

Step-by-step explanation:

I would use point wise plotting and then get a pattern from that and then simply draw the rest of the graph.

So let’s try 0: 0 + [0] = 0 + 0 = 0 ( so plot point (0,0) )

Now take .5 and we get .5 + [.5] = .5 + 0 = .5 ( so plot point (.5, .5)

Now take .9999 and we get .9999 + [.9999] = .9999 + 0 = .9999 ( so plot point (.9999, .9999) )

Now take 1 and we get 1 + [1] = 1 + 1 = 2 ( so plot the point (1,2) )

so I think we can see a bit of a pattern here between and including 0 and 1 excluding one. At (1,1) we have an open dot.

Now take 1.4 and we get 1.4 + [1.4] = 1.4 + 1 = 2.4 ( so plot the point (1.4,2.4) )

So I think it is safe to say the we can draw a diagonal line between 0 and 1, starting at 0 and ending at 1 with an open dot at 1. Next plot the point (1,2) and draw a diagonal between starting at (1,2) and going up to (2,3) with an open dot on (2,3).

The pattern is now clear and you can draw as much of the graph as you like.