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NY Regents Algebra II Rational Functions — practice questions

Explore 5 free Rational Functions questions in NY Regents Algebra II Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Rational Functions questions and exercises with answers

Showing questions 1–5 of 5.

A rational function is written as the quotient of two of what kind of function?Read the answer and worked solution →Which inputs must be left out of the domain of a rational function?Read the answer and worked solution →For f(x) = (6x squared + 5) divided by (3x squared - x + 2), what is the horizontal asymptote?Read the answer and worked solution →Find the vertical asymptotes of f(x) = (2x + 7) divided by (x squared - 4x).Read the answer and worked solution →Where does f(x) = (x squared - 9) divided by (x squared - 2x - 3) have a hole rather than an asymptote?Read the answer and worked solution →

Worked practice questions

A rational function is written as the quotient of two of what kind of function?

  1. Logarithmic functions
  2. Exponential functions
  3. Polynomial functions
  4. Absolute value rules
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Correct answer: C. Polynomial functions

1. A rational number is one integer over another integer. 2. A rational function copies that shape with functions instead of integers. 3. It is a quotient of two polynomial functions, and the denominator may not be the zero function. _Source: OpenStax Precalculus (CC BY 4.0), section 3.7 Rational Functions_

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Which inputs must be left out of the domain of a rational function?

  1. Those making the numerator 0
  2. Those making the denominator 0
  3. Those making the output negative
  4. Those making the input negative
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Correct answer: B. Those making the denominator 0

1. A rational function divides one polynomial by another. 2. Division by zero is undefined, so any input that makes the denominator 0 has no output. 3. The domain is therefore every real number except those values. 4. Inputs that make the numerator 0 are fine, since they simply give an output of 0. _Source: OpenStax Precalculus (CC BY 4.0), section 3.7 Rational Functions_

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For f(x) = (6x squared + 5) divided by (3x squared - x + 2), what is the horizontal asymptote?

  1. y = 3
  2. y = 0
  3. y = 2
  4. y = 6
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Correct answer: C. y = 2

1. Compare the degree of the top with the degree of the bottom. 2. Both are degree 2, so the asymptote is the ratio of the leading coefficients. 3. That ratio is 6 divided by 3, which is 2, so the asymptote is y = 2. 4. Answering y = 0 would apply the rule for a numerator of lower degree instead. _Source: OpenStax Precalculus (CC BY 4.0), section 3.7 Rational Functions_

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More Mathematics topics

Complex NumbersExponential and Logarithmic ModelsGraphs of Polynomial FunctionsPower and Polynomial FunctionsZeros of Polynomial FunctionsProperties of LogarithmsQuadratic FunctionsDividing Polynomials