Respuesta :
Yes, the specified function [tex]f(x) = \frac{1}{7} x - 4x^2 +4x^4 - 1[/tex] is a Polynomial Functions.
Polynomial Functions:
Polynomial functions are functions that take only non-negative integer powers or positive integer exponents of variables in equations such as quadratic, cubic, etc. For example, 2x+5 is a polynomial with exponent equal to 1.
There are different kinds of polynomial functions based on the degree of the polynomial. The most common types are:
- Constant polynomial function: P(x) = a = ax0
- Zero polynomial function: P(x) = 0; where ai are all zeros, i = 0, 1,…, n.
- Linear Polynomial function: P(x) = ax + b
- Quadratic polynomial function: P(x) = ax2+bx+c
- Cubic polynomial function: ax3+bx2+cx+d
- Quarter polynomial function: ax4+bx3 +cx2 +dx +e
According to the Question:
The standard form is
[tex]f(x) = 4x^4 -4x^2 + \frac{1}{7} x - 1[/tex]
The polynomial degree is 4.
Main coefficient is 4.
The given polynomial is
[tex]f(x) = \frac{1}{7} x - 4x^2 +4x^4 - 1[/tex]
Therefore, The standard form is
[tex]f(x) = 4x^4 -4x^2 + \frac{1}{7} x - 1[/tex]
The greatest power of the variable is known as the degree.
So the coefficient of the variable with the highest power of degree 4
is called the leading coefficient.
So the leading coefficient is 4.
Learn more about Polynomial Function:
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