5.2 – Evaluate and Graph Polynomial Functions

Recall that a monomial is a number, variable, or a product of numbers and variables. A

polynomial is a monomial or a sum of monomials.

A polynomial function is a function of the form:

5.2 – Evaluate and Graph Polynomial Functions

an cannot be zeroThe exponents are all whole numbers

Coefficients are all real numbers

an is the leading coefficientn is the degree

a0 is the constant termA polynomial is in standard form if its terms

are written in descending order of exponents.

5.2 – Evaluate and Graph Polynomial Functions

5.2 – Evaluate and Graph Polynomial Functions Example 1:

Decide whether the function is a polynomial function. If so, write it in standard form and

state its degree, type, and leading coefficient.

5.2 – Evaluate and Graph Polynomial Functions Example 2:

Use direct substitution to evaluate

f(x) = 2x4 – 5x3 – 4x + 8

when x = 3.

5.2 – Evaluate and Graph Polynomial Functions Example 3:

Use direct substitution to evaluate

f(x) = x4 + 2x3 +3x2 – 7

when x = -2.

5.2 – Evaluate and Graph Polynomial Functions

The end behavior of a function’s graph is the behavior of the graph as x approaches positive

infinity or negative infinity.

For the graph of a polynomial function, the end behavior is determined by the function’s

degree and the sign of its leading coefficient.

5.2 – Evaluate and Graph Polynomial Functions

5.2 – Evaluate and Graph Polynomial Functions

5.2 – Evaluate and Graph Polynomial Functions