Question

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

Answer 1

Answer:  The graphs are attached.

Step-by-step explanation:  We are to describe the graph of the function $y=\dfrac{1}{2x-10}-3$ compared to the graph of the function $y=\dfrac{1}{x}.$

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

We can see that the graph of the function $y=\dfrac{1}{2x-10}-3$ 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 $y=\dfrac{1}{x}.$

Answer 2

Answer:

The graph of $y=\frac{1}{2x-10}-3$ is the graph of $y=\frac{1}{x}$ stretched vertically, shifted right by 10 unit and shifted 3 unit down.

Step-by-step explanation:

Given : The graph of $y=\frac{1}{2x-10}-3$ compared to the graph of $y=\frac{1}{x}$  

To find : Describe the comparison of the graphs.

Solution :  

Let the parent function be$y_1=\frac{1}{x}$

Transformed function $y_2=\frac{1}{2x-10}-3$

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 $y_1=\frac{1}{x} \rightarrow \text{Vertically stretch by 2} \rightarrow \frac{1}{2x}$

Shifting right :  

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

Subtracting 10 means you are moving it right by 10 units  

$y_1=\frac{1}{2x} \rightarrow \text{Shifted right by 10 units} \rightarrow y_1=\frac{1}{2x-10}$

Shifting down :  

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

Subtracting 3 means you are moving it down by 3 units  

$y_1=\frac{1}{2x-10} \rightarrow \text{Shifted down by 3 units} \rightarrow y_1=\frac{1}{2x-10}-3=y_2$

Refer the attached figure below.  

The graph of $y=\frac{1}{2x-10}-3$ is the graph of $y=\frac{1}{x}$ stretched vertically, shifted right by 10 unit and shifted 3 unit down.