Transcript Key Concept: Function

Two Main Classes of
Elementary Functions (1/26/09)
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Algebraic functions. These are functions
in which the output comes starting with
the input variable and doing nothing
but combinations of powers, sums,
differences, products and quotients.
Transcendental functions. These are
function which are not algebraic.
Types of Algebraic Functions
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Linear functions
Polynomial functions
Power functions
Rational functions
Combinations of the above
Clicker Question 1
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The function f (x) = 3x + x is a
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A. linear function
B. polynomial function
C. power function
D. rational function
Types of
Transcendental Functions
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Trigonometric (“circular”, “periodic”)
functions
Exponential functions
Logarithmic functions
Others, including hyperbolic
Clicker Question 2
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The function g (x)= x 2 + 2x is a
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A. polynomial function
B. power function
C. rational function
D. transcendental function
Mathematical Models Again
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When applied mathematicians try to
model natural phenomena with
functions, they must pick the most
appropriate types of elementary
functions.
If possible, linear models are great
(easy to work with), but they often
don’t describe the situation accurately.
Examples
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Distance traveled by a car driving at a
constant rate.
Height of a ball thrown upwards.
Amount of daylight each day over a
year in Saratoga Springs.
Number of bacteria in a new culture.
Intensity of an earthquake.
Clicker Question 3
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What type of function would best model
the amount of money in an account
which earns 8% interest compounded
monthly?
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A. polynomial function
B. power function
C. trig function
D. exponential function
E. log function
Clicker Question 4
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What type of function would best model the
y – coordinate on a “unit circle” (i.e., a circle
of radius 1) as you move around the circle
counterclockwise starting at (1, 0)?
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A. polynomial function
B. power function
C. trig function
D. exponential function
E. log function
Assignment for Wednesday
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Read Section 1.2
Do Sec 1.2 Exercises 1, 3, 5, 7, 9, 13,
15, 17, 19, 20, 21 a and b.