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Find the vertical asymptotes of the function.

y =x² + 1/5x − 2x²

User BrandonS
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Final answer:

To find the vertical asymptotes of the given function, set the denominator equal to zero and solve for x. The vertical asymptotes are the values of x that make the denominator zero, which in this case are x = 0 and x = 9/5.

Step-by-step explanation:

To find the vertical asymptotes of the function y = x² + 1/5x - 2x², we need to consider the values of x that make the denominator of the function equal to zero.

In this case, the denominator is x² - 2x² + 1/5x. To find the values of x that make this denominator equal to zero, we can set it equal to zero and solve for x.

x² - 2x² + 1/5x = 0

To solve this quadratic equation, we can factor out x:

x(x - 2 + 1/5) = 0

So, we have x(x - 9/5) = 0

This equation has two solutions: x = 0 and x = 9/5.

Therefore, the vertical asymptotes of the function y = x² + 1/5x - 2x² are x = 0 and x = 9/5.

User Sandos
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