SOLUTION: Consider these functions: y= 2x-13/x-5 and y= 3x+11/x+3
a. Rewrite each rational function to show how it is a transformation of y= 1/x
b. describe the transformation of the graph
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-> SOLUTION: Consider these functions: y= 2x-13/x-5 and y= 3x+11/x+3
a. Rewrite each rational function to show how it is a transformation of y= 1/x
b. describe the transformation of the graph
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Question 822022: Consider these functions: y= 2x-13/x-5 and y= 3x+11/x+3
a. Rewrite each rational function to show how it is a transformation of y= 1/x
b. describe the transformation of the graph of y= 1/x that will produce graphs of the equation Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! First of all, please put parentheses around numerators and denominators, especially if they are not just a positive integer or variable. What you posted meant:
which is not a transformation from y = 1/x. What you meant must have been
which should be posted as:
y= (2x-13)/(x-5)
For part a we will start by using long division to divide:
2
__________
x - 5 / 2x - 13
2x - 10
--------
-3
So now we have:
Now we'll move some things around to make the transformations more obvious:
Let f(x) = 1/x. Then we can write:
Part b. The transformations:
The f(x-5) indicates a phase/horizontal shift/translation to the right by 5 units.
The +2 indicates a vertical shift/translation of up 2 units.
The minus of -3 indicates a reflection across the horizontal axis (which has been moved up to y = 2 by the vertical shift).
The 3 of -3 indicates a vertical stretching by a factor of 3.
Here's what the graphs look like (your function in red, f(x) = 1/x in green):
(