Which equation matches the graph of the greatest integer function given below?

a. y=[x]-3

b. y=[x]+1

c. y=[x]+3

d. y=[x]-1

C. y=[x]+3

Step-by-step explanation:

Let g(x) be the function of the given graph.

For which, the parent function is,

f(x) = [x]

In which, f(x) = 0 in the interval [0, 1)

But, according to the graph,

In the interval [0,1), g(x) = 3

⇒ F(x) is shifted vertically upward,

⇒  g(x) = f(x) + 3

⇒ g(x) = [x] + 3

Therefore, Option C is correct.

Pick a point and evaluate the functions to see which describes that point. If there are multiple functions that do, then pick another point.

Only selection C matches the graph at x=0.