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

Question

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. ƒ(x)=(x²-16)/(x+4)

Matching exercise with rational functions in Column I and their unique descriptions in Column II, including intercepts and asymptotes.

Accepted Answer

Hey, everyone. Here we are asked to write the coordinates of the whole. For the given function F of X is equal to X squared minus 36 all divided by the quantity of X plus six. Here we have four answer choice options. Each of which are some ordered pair. Where answer A is the ordered pair, negative six and negative 12. Answer B is six and negative 12. Answer C is negative six and 12 and answer D is six and 12. So to begin finding the coordinates of the whole four hour given function, we first want to start by factoring the numerator. So looking at the expression in the numerator, we have X squared minus 36. If we recall the difference of squares formula, we know that A squared minus B squared is equal to the quantity of A plus B multiplied by the quantity of A minus B. So now just comparing our difference of squares formula to our expression that we are trying to factor, we can notice that our value for A is going to be X and the value for B is going to be six. So this tells us that X squared minus 36 factors into the quantity of X plus six multiplied by the quantity of X minus six. So now we just want to substitute in this factored expression into our numerator of our function. And so our expression becomes the quantity of X plus six multiplied by the quantity of X minus six all divided by the quantity of X plus six. And now we can notice that we have a common factor of X plus six in both the numerator and the denominator of our expression. So we want to take this common factor and set it equal to zero and solve for X. So we have X plus six is equal to zero. And solving for X, we just subtract six from both sides. So we have X is equal to negative six. Now looking back at our expression, we want to simplify it by canceling out our common factor. So again, we have X plus six in the numerator which cancels with the X plus six in the denominator. So we find that our simplified expression is F of X is equal to X minus six. And so now we want to find the value of our function when X is equal to negative six. So finding F of negative six, we substitute in negative six into our simplified expression. So we have negative six minus six which gives us negative 12. And so this tells us we have the X value for our whole, which is at negative six. And then we have now the Y value which is negative 12. So we can write the ordered pair of our whole. So the coordinates of our whole are at negative six and negative 12. So with this ordered pair, we are left with answer choice. A where again, the coordinates of our whole are at negative six and negative 12. 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 description in Column II. Choices in Column II can be used only once. ƒ(x)=(x²-16)/(x+4)

Key Concepts

Rational Functions

Simplification and Factorization

Domain and Discontinuities

Watch next

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. ƒ(x)=(x2-16)/(x+4)

Key Concepts

Rational Functions

Simplification and Factorization

Domain and Discontinuities

Watch next

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. ƒ(x)=(x²-16)/(x+4)