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

2. 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)

3. 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!

4. 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.

5. 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

6. 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

7. 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!!

8. Homework
P3 worksheet 2-54 Even