Question

I am trying to graph a vertical shift for a greatest integer function

Answer 1

Step-by-step explanation

The graph of the parent function f(x) = [x] is

The function has the value of x until the next integer. So we have:

f(x) = 0 when x = 0 until x = 1, and then it changes to f(x) = 1. This is for all values of x. We can say that the function "jumps" on each integer and then keeps its value.

If we do a vertical shift of 2 units we have to add 2 to each value of the parent function. This way the shifted function is f(x) = 2 when x = 0 until x = 1, and then it jumps to f(x) = 3: