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Unit 1 Lesson 3 P.3 Functions and Graphs

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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


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