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NY Regents Algebra II Power and Polynomial Functions — practice questions

Explore 5 free Power and Polynomial 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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Power and Polynomial Functions questions and exercises with answers

Showing questions 1–5 of 5.

What is the degree of a polynomial function?Read the answer and worked solution →Why is f(x) = 2 raised to the power x not a power function?Read the answer and worked solution →Which term of a polynomial decides its end behaviour?Read the answer and worked solution →For f(x) = 5 + 2x cubed - 7x to the sixth + x, what is the leading coefficient?Read the answer and worked solution →Sort rules into polynomial or powerRead the answer and worked solution →

Worked practice questions

What is the degree of a polynomial function?

  1. Its count of separate terms
  2. Its coefficient on the last term
  3. Its value when the input is 0
  4. Its highest power of the variable
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Correct answer: D. Its highest power of the variable

1. Write the polynomial in general form, with powers descending. 2. The degree of the polynomial is the highest power of the variable that occurs in it. 3. The term carrying that highest power is the leading term, and its coefficient is the leading coefficient. _Source: OpenStax Precalculus (CC BY 4.0), section 3.3 Power Functions and Polynomial Functions_

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Why is f(x) = 2 raised to the power x not a power function?

  1. Its base is negative and cannot be used
  2. Its power is fixed but the base varies
  3. Its base is fixed and its power varies
  4. Its coefficient is 2 rather than 1
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Correct answer: C. Its base is fixed and its power varies

1. A power function has a variable base raised to a fixed power, such as x cubed. 2. In 2 raised to the power x the base 2 is fixed and the exponent x varies. 3. That is the reverse arrangement, so it is an exponential function rather than a power function. _Source: OpenStax Precalculus (CC BY 4.0), section 3.3 Power Functions and Polynomial Functions_

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Which term of a polynomial decides its end behaviour?

  1. The term of lowest degree
  2. The term with no variable
  3. The term with a negative sign
  4. The term of highest degree
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Correct answer: D. The term of highest degree

1. For very large or very small inputs, one term grows far faster than the rest. 2. That is the term with the highest power of the variable. 3. So the end behaviour of the whole polynomial matches the end behaviour of the term of highest degree. 4. The constant term shifts the graph but leaves the far left and far right unchanged. _Source: OpenStax Precalculus (CC BY 4.0), section 3.3 Power Functions and Polynomial Functions_

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More Mathematics topics

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