Distance, Circles Eric Hoffman Calculus PLHS Aug. 2007

Key Topics Power functions – functions of the form x n where n is a positive integer.

Key Topics Parabola – graph of a function in the form of ax 2 Quadratic functions : polynomial functions of the form f(x) = Ax 2 + Bx + C Polynomials : functions of the form a n x n + a n-1 x n-1 + … + a 1 x + a 0 where a 0, a 1, …, a 2 are constants, a n ≠ 0, and n is a positive integer Example: 3x 3 + 6x 2 – 3x + 4 Like quadratic functions polynomials are defined for all numbers x

Key Topics degree: the integer n is called the degree of the polynomial Note: the higher the degree of the polynomial, the greater number of “turns” in its graph What degree are the following functions: 8x 5 + 4x 4 + 5x 3 + 2x 2 + 7x x 3 + 4x 2 + 5x x x 6 + 7x + 23

Key Topics Rational functions: function of the form Note: domain or rational function excludes all numbers for which the denominator equals zero

Key Topics Power functions with n not an integer : power functions f(x) = x r, r = n/m Let x,y ε R and n,m ε Z + x n means x·x·x·x·x·x·x·x (n factors) x –n means x 1/n = y means y n = x

Key Topics Let x,y ε R and n,m ε Z + x m/n means (x 1/n ) m X 0 means 1 whenever x ≠ 0 Look at example 2 on page 47

Key Topics Laws of Exponents: x,y ε R and n,m ε Z x n · x m = x n+m = x n-m, x ≠ 0 (x n ) m = x nm x m/n = (x 1/n ) m = (x m ) 1/n, x ≥ 0 if n is even (xy) n = x n y n Example 3 on page 48