Question

PLEASE HELP
Describe the graph of y=1/2x-10 -3 compared to the graph of y=1/x

Answer 1

The graph of
`y=(1)/(2x-10)-3` is the graph of
`y=(1)/(x)` stretched vertically, shifted right by 10 unit and shifted 3 unit down.

Explanation:

Given : The graph of
`y=(1)/(2x-10)-3` compared to the graph of
`y=(1)/(x)`

To find : Describe the comparison of the graphs.

Solution :

Let the parent function be
`y_1=(1)/(x)`

Transformed function
`y_2=(1)/(2x-10)-3`

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
`y_1=(1)/(x) \rightarrow \text{Vertically stretch by 2} \rightarrow (1)/(2x)`

Shifting right :

f(x)→f(x-b), graph is transformed by b unit

Subtracting 10 means you are moving it right by 10 units

`y_1=(1)/(2x) \rightarrow \text{Shifted right by 10 units} \rightarrow y_1=(1)/(2x-10)`

Shifting down :

f(x)→f(x)-b , graph is transformed by b unit

Subtracting 3 means you are moving it down by 3 units

`y_1=(1)/(2x-10) \rightarrow \text{Shifted down by 3 units} \rightarrow y_1=(1)/(2x-10)-3=y_2`

Refer the attached figure below.

The graph of
`y=(1)/(2x-10)-3` is the graph of
`y=(1)/(x)` stretched vertically, shifted right by 10 unit and shifted 3 unit down.

Answer 2

Answer: The graphs are attached.

Step-by-step explanation: We are to describe the graph of the function
`y=(1)/(2x-10)-3` compared to the graph of the function
`y=(1)/(x).`

The graphs of both the functions are shown in the attached figure.

We can see that the graph of the function
`y=(1)/(2x-10)-3` 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
`y=(1)/(x).`