Chapter 1, Problem 9CR

To determine

To graph : The function is to be determined whose graph is the transformation of the given function which represents the translation 3 units down in the y-axis.

Explanation of Solution

Given information : The given function is $f(x)=x$

Graph : The function which is to be determined is given by $g(x)=-x-3$ which represents the translation 3 units down.

The graph of the given function $f(x)=x$ as shown below:

  

Graph of the transformed function $g(x)=-x-3$

  

Table for the above graph:

X(input)	-1	-2	0	1	2
Y(output)	-2	-1	-3	-4	-5

Transformation graph as shown below:

  

Interpretation :

The function which is the transformation of given function is $g(x)=-x-3$ which represents translation 3 units down in the y-axis. Also, the graph of the given function shows the parent function graph.