Question

If f(x) is the floor function, which answer shows the graph of g(x)=f(x+1)?

Answer 1

The floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x

Then it shapes like a stairs

Its starting points are black circles and its ending points are empty circles

The middle one is a line of length 1 unit starting from 0 to 1 [(0, 0), (1, 0)]

Since g(x) = f(x + 1)

That means we will move f(x) 1 unit to the left (subtract x-coordinate by 1)

Then the points (0, 0) [black point] and (1, 0) [empty point] will change to (-1, 0) [black point] and (0, 0) [empty point]

Let us look at these graphs and find the correct one

This is the correct answer because

It has a black circle at (-1, 0) and an empty circle at (0, 0)

This is the original figure of the floor function f(x)

Then when we translate it 1 unit to the left, every black point will move 1 unit to the left

Then the point (0, 0) will be (-1, 0) and the point (1, 0) will be (0, 0), then the correct option should be