Checkpoint: Polynomial Functions in One Variable Solution
Determine if the given functions represent a power and/or polynomial function, or neither.
Power and polynomial
There is one term raised to a fixed power.
Polynomial
The coefficients are real numbers, and the exponents are whole numbers.
Power
There is one term raised to a fixed fractional exponent.
Polynomial
The coefficients are real numbers, and the exponents are whole numbers.
Note
- Q: What is the degree of this function? Is it a fixed power?
A: One. Yes, the power, or exponent, does not change. - Because pi is a real number, this is a polynomial. Irrational values are still real.
- 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