Write two different rational functions whose graphs have the same end behavior as the graph of $$y=3x^2$$

nicekikah

nicekikah

Answered question

2021-06-17

Write two different rational functions whose graphs have the same end behavior as the graph of y=3x2

Answer & Explanation

unett

unett

Skilled2021-06-18Added 119 answers

y=3x2
Pick some factor to multiply top and bottom
y=3x2{x+2x+2=3x3+6x2x+2}
This adds a "hole" at x=2 simce that would be undefined, but otherwise behaves exactly like y=3x2 because of course the factors cancel out.
2. Pick another factor to multiply top and bottom
y=3x2{x5x5=3x315x2x5}
"Hole" at x=5, but otherwise the same as y=3x2.
A simpler option could be to just add some constant to 3x2

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