Chapter 1.6, Problem 42E

(a)

To determine

To graph: the given function $k\left(x\right)=4{\left(\frac{1}{2}x-\left[\frac{1}{2}x\right]\right)}^2$ .

Explanation of Solution

Given information:

Given function

  $k\left(x\right)=4{\left(\frac{1}{2}x-\left[\frac{1}{2}x\right]\right)}^2$

Calculation:

To sketch the graph of function $k\left(x\right)=4{\left(\frac{1}{2}x-\left[\frac{1}{2}x\right]\right)}^2$ in graphing calculator input the function

  $Y_1=4{\left(\frac{1}{2}x-\left[\frac{1}{2}x\right]\right)}^2$ or $Y_1=4{\left(0.5x-\left[0.5x\right]\right)}^2$

  

Press the graph key to obtain the graph. The graph of function $Y_1$ appears in window $\left[-9,9,X_{scl}=1\right]$ by $\left[-4,9,Y_{scl}=1\right]$ as shown below:

  

(b)

To determine

To state: the domain and range of the function..

Answer to Problem 42E

The domain of function is set of all integers or $\left(-\infty ,\infty \right)$ and range of function is $\left[0,4\right)$ .

Explanation of Solution

Given function is $k\left(x\right)=4{\left(\frac{1}{2}x-\left[\frac{1}{2}x\right]\right)}^2$

Consider the graph of the function.

  

The domain of function is set of all integers or $\left(-\infty ,\infty \right)$ and range of function is $\left[0,4\right)$ .