0. Functions

Common Functions

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Multiple Choice

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=4x^3+\frac12x^{-1}-2x+1$

Polynomial with $n=3,a_{n}=4$

Polynomial with $n=4,a_{n}=3$

Polynomial with $n=-1,a_{n}=\frac12$

Not a polynomial function.

Verified step by step guidance

Identify the terms in the function f(x) = 4x^3 + \frac{1}{2}x^{-1} - 2x + 1.

Recall that a polynomial function is a sum of terms of the form a_n x^n, where n is a non-negative integer and a_n is a coefficient.

Examine each term: 4x^3 is a polynomial term with n=3, -2x is a polynomial term with n=1, and 1 is a constant term with n=0.

Notice the term \frac{1}{2}x^{-1}. The exponent -1 is negative, which means this term is not a polynomial term.

Conclude that because the function includes a term with a negative exponent, it is not a polynomial function.

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Expert video explanations

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. f(x)=4x3+12x−1−2x+1f\left(x\right)=4x^3+\frac12x^{-1}-2x+1f(x)=4x3+21x−1−2x+1