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Aim: Review functions and their graphs

Aim: Review functions and their graphs. Do Now: 1. Which graph are functions? 2. Write the equations. 1. 2. 3. 6. 4. 5. 4. The vertical line test : If the graph of a relation pass the vertical line test then the relation is a function.

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Aim: Review functions and their graphs

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  1. Aim: Review functions and their graphs Do Now: 1. Which graph are functions? 2. Write the equations 1. 2. 3. 6. 4. 5. 4

  2. The vertical line test: If the graph of a relation pass the vertical line test then the relation is a function The horizontal line test: If the graph of a function pass the horizontal line test then the function whose inverse is also a function Domainis the set of first elements (x’s) Range is the set of second elements (y’s)

  3. Types of function: Polynomial function: + + + Exponential function: is the initial quantity, a is the factor by which P changes when t increase by 1, When a > 1is exponential growth, when 0 < a < 1 is exponential decay

  4. Logarithmic function: Common log: y = log x Natural log: y = ln x RULES of LOGARITHMS Product Rule:logbAB = logbA + logbB Quotient Rule:logbA/B = logb A - logbB Power Rule:logbAc= c logbA

  5. Properties of natural logarithms 1. lnex = x 2. elnx = x 3. ln 1 = 0, e0 = 1 4. lne = 1, e1 = e 5. If lnx = lny, then x = y

  6. Trigonometric function y = A sin B(x – C) + D or y = AcosB(x – C) + D is the amplitude, B is the frequency, C is the phase shift and D is the vertical shift Period =

  7. Power function has the form where k and p are constant Odd power functions Even power functions

  8. Find the domain and range of

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