Checkpoint: Polynomial Functions in One Variable Solution

Determine if the given functions represent a power and/or polynomial function, or neither.

  1.  y=x

Power and polynomial
There is one term raised to a fixed power.

  1. Ar=9πr2+12πr+4π

Polynomial
The coefficients are real numbers, and the exponents are whole numbers.

  1.  fx=x3 

Power
There is one term raised to a fixed fractional exponent.

  1.  y=35x6+14x5x42x

Polynomial
The coefficients are real numbers, and the exponents are whole numbers.

Note
  1. Q: What is the degree of this function? Is it a fixed power?
    A: One. Yes, the power, or exponent, does not change.
  2. Because pi is a real number, this is a polynomial. Irrational values are still real.
  3. Q: How can this radical be written using an exponent?
    A: x raised to the one-third power
    Q: Can this function be a polynomial function? Explain.
    A: No, because polynomial functions only have whole number exponents

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