Chapter 1.6, Problem 34E

To determine

Sketch the graph of the given function.

Answer to Problem 34E

Graph is shown below.

Explanation of Solution

Given:

The function,

  $g\left(x\right)=〚x-3〛$

Consider the function,

  $g\left(x\right)=〚x-3〛$

The greatest integer function $〚x〛$ gives greatest integer less than or equal to the x.

To plot the graph of above function find out some coordinates for this function by substituting the x coordinate and evaluating the y coordinate.

  $\begin{array}{l}Forx=0\hfill \\ g\left(x\right)=〚0-3〛\hfill \\ =〚-3〛\hfill \\ =–3\hfill \\ Forx=0.5,\hfill \\ g\left(x\right)=〚0.5-3〛\hfill \\ =〚-2.5〛\hfill \\ =–3\hfill \end{array}$

Therefore for $0\le x<1,g\left(x\right)=–3$

  $\begin{array}{l}Forx=1\hfill \\ g\left(x\right)=〚1-3〛\hfill \\ =〚-2〛\hfill \\ =–2\hfill \\ Forx=1.5,\hfill \\ g\left(x\right)=〚1.5-3〛\hfill \\ =〚-1.5〛\hfill \\ =–2\hfill \end{array}$

Therefore for $1\le x<2,g\left(x\right)=–2$

Similarly find out other points.

Draw the graph of function $g\left(x\right)$ as shown below,

  

Here solid point of black color indicates the included integer $x$ .