Polynomial Functions f(x) = a f(x) = ax + b f(x) = ax2 + bx + c Lesson: ____ Section: 2.2 Function Degree Graph f(x) = a f(x) = ax + b 1 f(x) = ax2 + bx + c 2 Horizontal line Line with slope a Parabola

Polynomial Functions Plot Points (table of values) How to graph a polynomial function (Helpful Hints): The x-int’s are called the zeros of the function. f(x) = 0 Plot Points (table of values) Locate the INTERCEPTS y-intercepts: (plug in x = 0) x-intercepts: (plug in y = 0) Use your knowledge of the following features:

1. The graph of a polynomial is CONTINUOUS. the pencil never leaves the paper (no jumps). 2. The graph has only SMOOTH TURNS (no corners) a function of degree n has at most n – 1 turns. If the leading coefficient is positive (a > 0), then the graph RISES to the RIGHT. As x  ∞, f(x)  ∞ (If a is negative, it falls to the right) As x  ∞, f(x)  -∞

Hmmm… If RIGHT behavior depends on the leading coefficient…. I wonder if I can draw a similar conclusion about LEFT behavior? Left behavior?

YOU CAN !!! LEFT behavior depends on both RIGHT behavior & the degree of the polynomial. Let me give you an example! Left behavior!

Even degree Even/odd examples Odd degree

Let’s try some examples! Thanks for the help!  Let’s try some examples! y = (- 1/5) x3+ 2x2-3x-4 y = 3x3 – 9x + 1 Y = 3x4 + 4x Y = x5 - 5x3 + 4x Problems