MATH 10A Lecture Notes - Lecture 5: Coefficient
Document Summary
Definition: the degree of a polynomial is the highest exponent that appears. Example of a polynomial: y = x2 + 2x - 7 y = 100 - 40x5 y = 5. Fact: a degree-n polynomial has at most n-1 turning points. If leading coefficient is, then the graph goes. Fact: a polynomial f(x) has an x-intercept at c if and only if (x-c) is a factor of f(x). As x ->0 from the right, y -> As x ->0 from the left, y -> - Example: determine the end behavior of (a) a(x) = (80 + 6x)/2x (b) b(x) = (80 + 6x)/2x2 (c) c(x) = (80 + 6x2)/2x. , 80/x -> 0, so a(x) -> 3. , 80/x2 -> 0, and 6/x -> 0, so b(x) ->0. Example: y = (x2 - 6x + 8) / (x - 2) The graph has a hole at the point (2, -2).
