Rational Functions Asymptotes

What is the definition of a rational function?

• A rational function is a function that can be written as the sum of two polynomial functions.

• A rational function is a function that can be written as the product of two polynomial functions.

• A rational function is a function that can be written as the difference of two polynomial functions.

• A rational function is a function that can be written as the quotient of two polynomial functions, where the denominator is not equal to zero.

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CCSS.HSF-IF.C.7D

What is an asymptote in the context of rational functions?

• A line that a graph approaches but never touches or crosses.

• A line that a graph crosses at one point.

• A line that a graph touches at one point.

• A line that a graph intersects at multiple points.

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CCSS.HSF-IF.C.7D

What are the two types of asymptotes that a rational function can have?

• vertical and horizontal

• positive and negative

• curved and straight

• oblique and diagonal

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CCSS.HSF-IF.C.7D

How can you determine the vertical asymptotes of a rational function?

• Find the values of x that make the denominator of the function equal to zero.

• Identify the values of x that make the function equal to zero.

• Determine the values of x that make the function undefined.

• Find the values of x that make the numerator of the function equal to zero.

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CCSS.HSF-IF.C.7D

How can you determine the horizontal asymptotes of a rational function?

• Compare the degrees of the numerator and denominator

• Evaluate the function at x = 0

• Find the x-intercepts of the function

• Take the derivative of the function

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CCSS.HSF-IF.C.7D

What is the equation of a vertical asymptote for a rational function?

• x = -a

• x = 0

• x = a

• x = 1/a

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CCSS.HSF-IF.C.7D

What is the equation of a horizontal asymptote for a rational function?

• y = x

• y = 0

• y = 1

• y = c

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CCSS.HSF-IF.C.7D

What is the difference between a removable and non-removable discontinuity in a rational function?

• A removable discontinuity can be filled by assigning a value to the function at that point, while a non-removable discontinuity cannot be filled by assigning a value to the function at that point.

• A removable discontinuity can be filled by removing a value from the function at that point, while a non-removable discontinuity cannot be filled by removing a value from the function at that point.

• A removable discontinuity occurs when the function is undefined at a certain point, while a non-removable discontinuity occurs when the function is defined at a certain point.

• A removable discontinuity can be fixed by changing the function's equation, while a non-removable discontinuity cannot be fixed by changing the function's equation.

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CCSS.HSF-IF.C.7D

How can you find the x-intercepts of a rational function?

• Set the denominator equal to zero and solve for x.

• Set the numerator equal to zero and solve for x.

• Set the whole function equal to zero and solve for x.

• Take the derivative of the function and find the x-values where the derivative is zero.

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CCSS.HSF-IF.C.7D

How can you find the y-intercept of a rational function?

• Set y = 0 and solve for x

• Set x = 1 and solve for y

• Find the slope of the function

• Set x = 0 and solve for y

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CCSS.HSF-IF.C.7D