Graphing Polynomial Functions 1 To graph, we will need to understand 4 main ideas: 1. What a ___________________ is 2. What ____________ are (Minimum and Maximum) 3. What _______________ is 4. What the _________/____________/________ are A polynomial function is a function of the form: = ! ! where: a is called the _____________________n is called ________________ When the function is written with terms in descending order of exponents, we say the function is _________________________________. We decide whether the function is a polynomial function and state its degree and leading coefficient. Examples: = 2 ! 4 ! = 3 ! ! ! = 3 ! ! ! Graphing Polynomials The graph of a polynomial function is always a smooth curve; that is, it has no breaks or corners: These graphs ______ polynomial graphs! These graphs _______polynomial graphs! Extrema and Roots (zeros) __________: Absolute vs. Relative (local) __________: Absolute vs. Relative (local) _____________: Where crosses x-axis (also called the x-intercept) End Behavior We can see that the DEGREE and LEADING COEFFICIENT control the shape of the graph! Match the function to the graph using its end behavior. 1. f ( x ) = x 33