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TEA [102]
3 years ago
8

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

Mathematics
2 answers:
jek_recluse [69]3 years ago
8 0

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}.

Artist 52 [7]3 years ago
4 0

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 bey_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.

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