Understanding Rational Functions and Asymptotes

What is a rational function?

• A function expressed as the quotient of two polynomials

• A function that only includes positive numbers

• A function that cannot have zero in the denominator

• A function with only integer coefficients

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CCSS.HSF-IF.C.7D

Why is zero excluded from the domain of the function 1/x?

• Because it simplifies the function to one

• Because it makes the function undefined

• Because it turns the function into a polynomial

• Because it results in a negative value

What does the function 1/x approach as x approaches zero from the positive side?

• Negative infinity

• One

• Positive infinity

• Zero

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CCSS.HSF-IF.C.7E

What are vertical asymptotes in the context of rational functions?

• Values that the function can never reach

• Maximum values of the function

• x-values where the function touches the x-axis

• y-values that the function approaches as x increases

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CCSS.HSF-IF.C.7D

How can you determine the presence of a horizontal asymptote?

• By comparing the degrees of the numerator and the denominator

• By calculating the derivative of the function

• By setting the denominator equal to zero

• By finding the zeros of the numerator

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CCSS.HSF-IF.C.7D

What does a higher degree in the denominator compared to the numerator indicate about horizontal asymptotes?

• The function will have multiple horizontal asymptotes

• The function will cross the y-axis multiple times

• Y equals zero is the horizontal asymptote

• There is no horizontal asymptote

Tags

CCSS.HSF-IF.C.7D

What is the effect of a vertical shift in the graph of a rational function?

• It moves the graph up or down

• It moves the graph left or right

• It stretches or compresses the graph vertically

• It rotates the graph around the origin

Tags

CCSS.HSF-IF.C.7D

Which method helps in sketching the behavior of a rational function near its asymptotes?

• Ignoring the asymptotes

• Extending the function to infinity

• Using only the intercepts

• Plotting points close to the asymptotes

Tags

CCSS.HSF-IF.C.7D