Question

Which function is represented by the graph?

Answer 1

its either a or b, but what does those signs around x means

Answer 2

The correct option is 2.

Explanation:

Greatest integer function is defined as

`\left \lfloor x \right \rfloor=\begin{cases}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}`

where, n is an integer.

Least integer function is defined as

`\left \lceil x \right \rceil=\begin{cases}0 & \text{ if } -1< x\leq 0 \\ 1 & \text{ if } 0< x\leq 1 \\ ... & \text{ if } ... \\ n& \text{ if } n-1< x\leq n\end{cases}`

From the given graph it is clear that it is a graph of greatest integer function because the we have open circles on the right side of each floor and closed circle on the left side of each floor.

The given graph is defined as

`g(x)=\begin{cases}2 & \text{ if } 0\leq x<1 \\ 3 & \text{ if } 1\leq x<2 \\ ... & \text{ if } ... \\ n+2& \text{ if } n\leq x<n+1\end{cases}`

Graph of greatest integer function shifts 2 units up.

`g(x)=\left \lfloor x \right \rfloor+2`

Therefore the correct option is 2.