Chapter 1.4, Problem 24E

To determine

To compare the graph of the given function with the parent function

Explanation of Solution

Given:

The given function is:

  $f(x)=\frac{1}{x}-5$

Calculation for graph:

Consider $f(x)=\frac{1}{x}-5$

Values of x	Values of f (x )
1/2	-3
1	-4
3	-4.67
2	-4.5
-2	-5.5

Using the above table the graph can be plotted.

Graph:

  

Interpretation:

Hence, the parent function will be $g(x)=\frac{1}{x}$ .

Calculation for graph:

Consider $g(x)=\frac{1}{x}$

Values of x	Values of g (x )
1	1
-1	-1
-2	-0.5
2	0.5
3	0.33

Using the above table the graph can be plotted:

Graph:

  

Interpretation:

To compare the functions, the graph of both $f(x)$ and $g(x)$ are plotted on a same co-ordinate plane.

Graph:

  

Interpretation:

From the above graph, it is clear that,

  $f(x)$ is the rigid transformation of the parent function $g(x)$ with a vertical shift of 5 units downwards.