Chapter 1, Problem 16CT

(a)

To determine

To identify: the parent function in the given transformation.

Explanation of Solution

Given information:

Consider function $h(x)=4[[x]]$

The parent function is the simple function which is having same shape as that of family

of curves.

  $h(x)=4[[x]]$

Hence, the parent function is $f(x)=[[x]]$

(b)

To determine

To describe: the sequence of transformations from f to h.

Explanation of Solution

Given information:

Consider function $h(x)=4[[x]]$

Graph:

The parent function $f(x)=[[x]]$

If the parent function $f(x)=[[x]]$ is vertically stretched by the factor $4$ then we obtain

the function $h(x)=4[[x]]$

Hence, the transformation from f to h is vertically stretched by the factor$4$

(c)

To determine

To sketch: the graph of h .

Explanation of Solution

Given information:

Consider function $h(x)=4[[x]]$

Graph:

Make a table of values

$x$	$0$	$0.5$	$1$	$1.5$	$2$	$2.5$
$h(x)=4[[x]]$	$0$	$0$	$4$	$4$	$8$	$8$

The graph of $h(x)=4[[x]]$ is shown below.