aim: review functions and their graphs

Aim: Review functions and their graphs

Do Now: 1. Which graph are functions? 2. Write the equations

4

1. 2. 3.

4. 5.6.

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

Domain is the set of first elements (x’s)

Range is the set of second elements (y’s)

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

Logarithmic function:

Common log: y = log x Natural log: y = ln x

RULES of LOGARITHMS

Product Rule: logb AB = logb A + logb B

Quotient Rule: logb A/B = logb A - logb B

Power Rule: logb Ac = c logb A

Properties of natural logarithms

1. ln ex = x 2. eln x = x

3. ln 1 = 0, e0 = 1 4. ln e = 1, e1 = e

5. If ln x = ln y, then x = y

Trigonometric function

y = A sin B(x – C) + D

is the amplitude, B is the frequency, C is the phase shift and D is the vertical shift

Period =

y = A cos B(x – C) + Dor

Power function has the form

where k and p are constant

Odd power functions Even power functions

Find the domain and range of