Q. 67 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $39-68$, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, $y=x^2$) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.Verify your results using a graphing utility.

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

Step-by-Step Solution

Answer

The graph of the function $h\left(x\right)=2int(x-1)$ is:

The domain and the range is the set of all real numbers.

Step 1. Given

The function $h\left(x\right)=2int(x-1)$

To graph the function and to find its domain and range.

Step 2. Graph the basic function

Graph the basic function $h\left(x\right)=int x$

Step 3. Replace i n t ( x ) with i n t ( x - 1 )

Replace $h\left(x\right)=int\left(x\right)$ by

              $h\left(x\right)=int(x-1)$, so that the graph shifted horizontally right to $1$ unit.

Step 4. Multiply the right side by 2

Multiply the graph $h\left(x\right)=int(x-1)$ by $2$, so that the graph stretched vertically by the factor $2$.

Step 5. Verify the graph

Verify the graph by using graphing utility.

The graph of the function using graphing utility is: