Chapter 2.5, Problem 61AYU

To determine

To sketch: graph of the given function using technique of transformation. Also find the domain and range.

Answer to Problem 61AYU

Domain of the function is all real numbers and range of the function is all real numbers.

Explanation of Solution

Given information:

Given function

  $h\left(x\right)=2\mathrm{int}\left(x-1\right)$

Calculation:

Step 1: The basic function here is $h\left(x\right)=\mathrm{int}x$ . Its graph is as follows.

  

Step 2: Replace $x$ by $x-1$ on the right side of the function $h\left(x\right)=\mathrm{int}x$ .

  $h\left(x\right)=\mathrm{int}\left(x-1\right)$

The graph of $h\left(x\right)=\mathrm{int}\left(x-1\right)$ is obtained by horizontally shifting the graph of $h\left(x\right)=\mathrm{int}x$ to the right by 1 unit.

  

Step 3: Multiply the right side of the function by 2.

  $h\left(x\right)=2\mathrm{int}\left(x-1\right)$

The graph of $h\left(x\right)=2\mathrm{int}\left(x-1\right)$ is the vertically stretched version of the graph of $h\left(x\right)=\mathrm{int}\left(x-1\right)$ by a factor of 2.

  

Domain of the function is all real numbers and range of the function is all real numbers.