3.1 Functions and Function Notation A circle is not a function: A parabola is a function:	Vertical Line Test: (Example is a function) If a vertical line passes through a graph throughout its domain only at one point then that graph is a function. Domain: The possible values of x Range: The possible values of y One-to-one Functions: Passes the Horizontal Line test
3.2 Quadratic Functions (parabolas)	The function is a parabola ( ) and the vertex is at (h, k). (see Complete the Square) The parabola or quadratic function as: 1. A maximum point is a < 0 2. A minimum point is a > 0 The function is a parabola with vertex at:
3.3 Polynomial and Other Functions Symmetry about the y-axis: Symmetry about the origin when:	Even function: when , usually powers of x are all even; symmetry about the y-axis Example: Odd function: when ; symmetry about the origin: Example: let Then
3.4 Translation and Stretching Graphs	By Example: Let then Horizontal Shift Right by h : Horizontal Shift Left by h : Vertical Shift Up by h : Vertical Shift Down by h : n Vertical Expansion by factor of a : Vertical Compression by factor of a :
3.5 Rational Functions	Rational Function: P(x) and Q(x) are polynomials To graph: Step 1: Check for symmetry Step 2: Find and draw Vertical Asymptote(s): Q(x) Step 3: Find and plot y-intercepts (when x = 0) and x-intercept(s) when P(x) = 0 Step 4: Find and draw horizontal asymptote (y as )
3.6 Operations on Functions	By Example: Let
3.7 Inverse Functions	For a one-to-one function there exists an inverse function such that: Both graphs are symmetrical about the line y = x The Domain of is the Range of and The Range of is the Domain of Example: Let and its inverse function For : Domain is and Range: For : Domain is and Range: