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Sladkaya [172]
3 years ago
9

Give an example of a rational function that has a horizontal asymptote of y = 2/9.

Mathematics
1 answer:
stiv31 [10]3 years ago
4 0
Note that the graph of the function \displaystyle{ f(x)= \frac{1}{x} has 2 asymptotes:

The horizontal asymptote x=0, 

and the vertical asymptote y=0, as shown in the first picture.


Adding 2/9 to this function, creating \displaystyle{ g(x)= \frac{1}{x}+\frac{2}{9}, shifts the first graph 2/9 units up. It also shifts the horizontal asymptote y=0 to t=2/9.

We can express the function as \displaystyle{ \frac{1}{x}+ \frac{2}{9}= \frac{9}{9x}+ \frac{2x}{9x}= \frac{2x+9}{9x}.


Answer: \displaystyle{ \frac{2x+9}{9x}


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