Unit 1 Lesson 3 P.3 Functions and Graphs AP Calculus Mrs. Mongold

Forms of Equations Implicit Form Explicit Form Function Notation x2 + 2y = 1 Explicit Form y = ½ (1 - x2) Function Notation f(x) = ½ ( 1 – x2)

Evaluating Functions Find f(2) , f( b +1), f( 3a), and f( Δx), and f(Θ) are all possibilities for values for a function Substitute these in to the function f(x) and simplify completely Don’t forget how to foil, factor, and combine like terms, Algebra is your friend!

Domain and Range Domain: input, usually x Range: output, usually y Remember your rules for piecewise functions, rational functions, and TRIG functions AP CALC Test does not have a formula sheet so you need know your TRIG forward, backward, and upside down.

Characteristics One-to-one Vertical Line Test General Shape of everything: lines, parabolas, cubics, square roots, absolute values, rational, exponential, trig functions and their inverses. Transformations – looking at a graph or an equation Even and Odd and End Behavior

Composite Functions f ο g and g ο f Again, Algebra kills here with mistakes, remember to foil, factor, simplify, and all your properties for exponents Also remember about domain and range, especially with trig functions and composites

Even vs Odd and Zeros A function is even if f(-x) = f(x) A function is odd if f(-x) = -f(x) Remember to FACTOR when finding zeros and that dividing by a variable is NEVER ok and keeping your domain in mind when finding zeros is important!!

Homework P3 worksheet 2-54 Even