polynomial function examples

For example, if a quadratic has roots x = 3 and x = −2, then the function must be f(x) = (x−3)(x+2), or a constant multiple of this This can be extended to polynomials of any degree

Examples f(x) 4x2 3x 2 n 2, a0 4, a1 3, a2 2 If you know an element in the domain of any polynomial function, you can find the corresponding value in the 

A polynomial function is a function of the form f(x) = anxn + an-1xn-1 + + a2x2 + a1x + a0, where a0, a1, , an are real numbers and n ≥ 1 is a natural number The domain of a polynomial function is (−∞,∞)

In the next example, we use our knowledge of polynomials and their graphs to analyze a fourth-degree polynomial Analyzing a Polynomial Function Perform the 

The answer is 2x, so we can write: 2x2 + x +1= 2x(x + 2) + remainder 2x2 + x + 1 x + 2 , as the polynomial in the numerator has degree 1 However, we can obtain a even simpler rational function that has only a constant in the numerator

The domain of all polynomial functions is all real numbers: (−∞,∞) The range depends on the polynomial 4 Page 5 Definition: The zeros of a function 

E X A M P L E Graphing Higher-Degree Polynomials on a Calculator Graph each polynomial function on a calculator Describe the graph, and identify the 

18 juil 2005 · Functions containing other operations, such as square roots, are not polynomials For example, f(x)=4x3 + √x − 1 is not a polynomial as it 

Students apply these techniques in solving word problems They also solve quadratic equations in the complex number system 10 0 Students graph quadratic 

5 mar 2014 · A specific equation for a polynomial function can be determined if a point on the graph is known Example One The zeros of a family of cubic