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^2-16)/(x+4)

Accepted Answer

Hey, everyone here we are asked to write the coordinates of the whole. For the following function F of X is equal to the quantity of X squared minus 36 divided by the quantity of X plus six. Here we have four answer choice options, answer A, the point negative six and negative 12. Answer B V 120.6, negative 12, answer CV point negative 6 12 and answer D V 120.6 12. So here with our given function, we see that in the numerator, we have the difference of two squares. So our first step is to just factor the numerator. So again, in the numerator, we have X squared minus 36. And if we recall the difference of squares formula, we know that A squared minus B squared is equivalent to the quantity of, of A plus B times the quantity of A minus B. So now utilizing this formula to factor our numerator, we get the factored form of the quantity of X plus six times the quantity of X minus six. So now we just want to substitute in this factored form into our function. So we have F of X is equal to the quantity of X plus six times the quantity of X minus six all divided by the quantity of X plus six. So now we see here in the numerator and the denominator, we have a common factor of X plus six. So we want to take this common factor which again is X plus six and set it equal to zero and solve for X. So solving for X, all we need to do is subtract six from both sides and we get X is equal to negative six. Now we can simplify the function that we have here because again, we have this common factor which will cancel in both the numerator and the denominator. So now just simplifying our function, we are left with F of X is equal to X minus six. And now with this value of X being equal to negative six. From earlier, we want to now substitute in this value into our function and find the value that results from X is equal to negative six. So finding F of ne six, we get the expression negative six minus six. In simplifying we get negative 12. And so with these two values, we see our Y is then equal to negative 12 when X is equal to negative six. So we are left with the point negative six and which serve at the point of the whole. So with this coordinate point, we are left with answer choice A where again, the hole is located at negative six and negative 12. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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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^2-16)/(x+4)