Question

Which graph represents the step function f(x)=⌊x+1⌋ ?

Answer 1

I believe it is this graph. I know because I used desmos calculator and the equation passed through all the points on this graph. I hope this helps

Answer 2

The correct option is 2.

Explanation:

The given function is

`f(x)=\left \lfloor x+1 \right \rfloor`

It is a greatest integer function.

The parent greatest integer function is

`g(x)=\left \lfloor x\right \rfloor`

This function is defined as

`g(x)=\left \lfloor x \right \rfloor=\begin{cases}-1 & \text{ if } -1\leq x<0 \\ 0 & \text{ if } 0\leq x<1 \\ 1 & \text{ if } 1\leq x<2 \\ ... & \text{ if }... \\ n & \text{ if } n\leq x<n+1 \end{cases}`

The parent function shifts 1 units up to get the given function.

`f(x)=\left \lfloor x+1 \right \rfloor=\begin{cases}0 & \text{ if } -1\leq x<0 \\ 1 & \text{ if } 0\leq x<1 \\ 2 & \text{ if } 1\leq x<2 \\ ... & \text{ if }... \\ n+1 & \text{ if } n\leq x<n+1 \end{cases}`

Left end of each floor is a closed circle because the sign of inequality is ≤ and right end of each floor is an open circle because the sign of inequality is <.

Therefore the correct option is 2.