aim: review functions and their graphs
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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. - PowerPoint PPT PresentationTRANSCRIPT
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