Answer: The graphs are attached.
Step-by-step explanation: We are to describe the graph of the function [tex]y=\dfrac{1}{2x-10}-3[/tex] compared to the graph of the function [tex]y=\dfrac{1}{x}.[/tex]
The graphs of both the functions are shown in the attached figure.
We can see that the graph of the function [tex]y=\dfrac{1}{2x-10}-3[/tex] is stretched by a factor of 0.5, shifted 5 units to the right and 3 units downwards as compared to the graph of the function [tex]y=\dfrac{1}{x}.[/tex]
Answer:
The graph of [tex]y=\frac{1}{2x-10}-3[/tex] is the graph of [tex]y=\frac{1}{x}[/tex] stretched vertically, shifted right by 10 unit and shifted 3 unit down.
Step-by-step explanation:
Given : The graph of [tex]y=\frac{1}{2x-10}-3[/tex] compared to the graph of [tex]y=\frac{1}{x}[/tex]
To find : Describe the comparison of the graphs.
Solution :
Let the parent function be[tex]y_1=\frac{1}{x}[/tex]
Transformed function [tex]y_2=\frac{1}{2x-10}-3[/tex]
Vertically Stretch:
If y =f(x) , then y= a f(x) gives a vertical stretch if a> 1.
Multiplying the parent function by 2 means you are stretching it vertically,
i,e [tex]y_1=\frac{1}{x} \rightarrow \text{Vertically stretch by 2} \rightarrow \frac{1}{2x} [/tex]
Shifting right :
f(x)→f(x-b), graph is transformed by b unit
Subtracting 10 means you are moving it right by 10 units
[tex]y_1=\frac{1}{2x} \rightarrow \text{Shifted right by 10 units} \rightarrow y_1=\frac{1}{2x-10}[/tex]
Shifting down :
f(x)→f(x)-b , graph is transformed by b unit
Subtracting 3 means you are moving it down by 3 units
[tex]y_1=\frac{1}{2x-10} \rightarrow \text{Shifted down by 3 units} \rightarrow y_1=\frac{1}{2x-10}-3=y_2[/tex]
Refer the attached figure below.
The graph of [tex]y=\frac{1}{2x-10}-3[/tex] is the graph of [tex]y=\frac{1}{x}[/tex] stretched vertically, shifted right by 10 unit and shifted 3 unit down.
