Question

Which of the following is a polynomial function? Select all correct answers. Select all that apply: f(x)=4⋅11x f(x)=3⋅18x f(x)=10⋅17x f(x)=−4x3−4x2+5x+1 f(x)=−2x−1

Answer 1

Answer:

All of them are polynomial functions

Step-by-step explanation:

Remember that a polynomial function of x is a function whose value f(x) is always equal to $f(x)=a_0+a_1x+a_2x^2+\cdots a_nx^n$ for a fixed n≥0 (the degree of f) and fixed coefficients $a_i\in\mathbb{R}$

For example, $f(x)=x^2+3x$ is a polynomial function, but $g(x)=2^x+x$ is not because $2^n$ is not a nonnegative power of x. Another example of a non-polynomial function is $g(x)=x^{-1}=\frac{1}{x}$.

f(x)=4⋅11x is polynomial with degree 1 and $a_0=0,a_1=4\cdot 11$. For the same reasons, f(x)=3⋅18x and f(x)=10⋅17x are polynomial functions.

f(x)=−4x³−4x²+5x+1 is a polynomial function of degree 3 with $a_0=1,a_1=5, a_2=a_3=-4$. and f(x)=−2x−1 is a polynomial function of degree 1 and coefficients $a_0=-1,a_1=-2$.