1. 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:

2. 5.2 – Evaluate and Graph Polynomial Functions a n cannot be zero The exponents are all whole numbers Coefficients are all real numbers a n is the leading coefficient n is the degree a 0 is the constant term A polynomial is in standard form if its terms are written in descending order of exponents.

3. 5.2 – Evaluate and Graph Polynomial Functions

4. 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. 5.2 – Evaluate and Graph Polynomial Functions Example 2: Use direct substitution to evaluate f(x) = 2x 4 – 5x 3 – 4x + 8 when x = 3.

6. 5.2 – Evaluate and Graph Polynomial Functions Example 3: Use direct substitution to evaluate f(x) = x 4 + 2x 3 +3x 2 – 7 when x = -2.

7. 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.

8. 5.2 – Evaluate and Graph Polynomial Functions