Match the rational function in Column I with the appropriate desc...

Question

Match the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=(x^2+3x+4)/(x-5)

Accepted Answer

Hey, everyone here we are asked to write the equation for the oblique Asymptote. For the given function F of X is equal to the quantity of X squared plus A X plus 13 all divided by the quantity of X minus three. Here we have four answer choice options. Answer A Y is equal to X plus 11. Answer B Y is equal to X minus 11. Answer C Y is equal to two X plus and answer D Y is equal to three X plus 11. So here, our first step in this problem is to verify that we do in fact have an oblique Asymptote. So we need to compare the degree in the numerator with the degree in the denominator. So looking at the numerator, we see the highest degree of X is two. And then in the denominator, we see that the highest degree of X is just one. So in conclusion, the degree of the numerator is exactly one greater than the degree of the denominator. Therefore, we know that there is in fact an oblique Asymptote. So since we have an oblique Asymptote, we can begin finding it and we do this by simply dividing the numerator by the denominator. So setting up this expression in long division formatting, we first have a bar place where the dividend is the numerator and we place it underneath the bar. So under the bar, we have X squared plus eight X plus 13. And now our divisor, the denominator is placed on the left side, on the outside, we have X minus three. And so now we can begin performing long division. So we take our first term in the dividend which is X squared and divide it by the highest degree of the divisor which is X. So we have X squared divided by X which gives us X. And now we take X and multiply it by X minus three which gives us X squared minus three X. And now we subtract this expression from X from the dividend. So we have X squared plus eight X plus 13 minus the quantity of X squared minus three X. So now subtracting, we see that the X squares cancel and we get zero, then we have eight X minus negative three which gives us plus 11 X just bringing down the last term we have plus 13. So now we repeat this process now taking 11 X and dividing it by X, which gives us plus 11, which we write at the top of the bar. And now we multiply 11 by our divisor. So we get 11 X minus and now we subtract this expression. So we have 11 X plus 13 minus the quantity of 11 X minus 33. So now subtracting, we see the 11 X S cancel and we get zero, we then have 13 minus negative 33 which gives us plus 46. And now this plus 46 is just our remainder which we can disregard because if we recall the oblique Asymptote is given as the equation Y is equal to the quotient. So since we just need the quotient, we see that we just take the expression at the top of the bar from after we performed long division. And so we see that our oblique Asymptote is Y is equal to X plus 11. Therefore, we are left with answer choice. A where again, our oblique asom tote is Y is equal to X plus 11. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Match the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=(x^2+3x+4)/(x-5)

Key Concepts

Rational Functions

Domain of a Function

Vertical and Horizontal Asymptotes

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