QQuestionMathematics
QuestionMathematics
"If there is a slant asymptote find its equation by dividing the numerator by the denominator
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Step 1Sure, I'd be happy to help you understand how to find the equation of a slant asymptote for a rational function!
That's it! The equation of the slant asymptote is $$y = x + 3$$.
A slant asymptote is a linear function that the graph of a rational function approaches as the values of the independent variable get larger and larger. To find the equation of a slant asymptote, we perform polynomial long division of the numerator by the denominator. Let's consider the following rational function as an example: **Step 1:** Perform polynomial long division of the numerator by the denominator. We can divide the terms of the numerator by the terms of the denominator as follows: So we can write the function as: **Step 2:** Identify the slant asymptote. The slant asymptote is the first part of the expression we obtained in Step 1, which is a linear function: **
Final Answer
I hope this helps you understand how to find the equation of a slant asymptote for a rational function! Let me know if you have any questions or if you'd like to see more examples.
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