re-introduction to functions
TRANSCRIPT
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In everyday life, many quantities depend on
one or more changing variables:C an you think of any examples?C an you think of any examples?
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H ow functions look asH ow functions look as
formulas,formulas,V = IR w here
V = voltage (V)
I = current (A)
R = resistance ( )
If I increases, so does thevoltage (assuming resistanceis constant).
If R increases, so does thevoltage (assuming current isconstant).
w here
s = speed (m / s)
d = distance (m)
t = time taken (s)
If d increases, the speed goes up (assumingtime is constant).
If t increases, the speed goes down(assuming distance is constant).
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M ore on functionM ore on function
definitions...definitions...W henever a relationship exists bet w een t w o variables (or quantities) such that for every value of the first, there is
only one corresponding value of the second, then w e say:"The second variable is a fu nction of the first variable."
The first variable is the ind epen d en t variable (usually x),
and the second variable is the d epen d en t variable (usuallyy).
The independent variable and the dependent variable arer eal numbe rs .
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R angeR ange
^II
IndependentIndependent
^II
DependentDependent
Function M achineFunction M achine
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Function NotationFunction NotationW e normally w rite functions as: f (x) and read this as"function f of x".
W e can use other letters for functions. Common ones areg (x) and h(x). But there are also ones like P (t ) w hich couldindicate p ower at time t .
Example:
If h(x) = dx3 + 5x then value of h(x) for x = 10 is:
h(10) = d (10) 3 + 5(10)
= 1000 d + 50
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E xamples:E xamples:C heck out these links for example homeworkC heck out these links for example homework
problems tonight....problems tonight....
Click and scroll down!
Click and scroll down!
F u nctions f rom Verbal Statements
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T he Family of Functions...GraphsT he Family of Functions...GraphsS ince there is no limit to the possible number of points for the graph of the function, w e w ill follo w this procedure at first: - - selectselecta fe w values of a fe w values of xx -- obtain the corresponding values of the functionobtain the corresponding values of the function - - plot these points by joining them w ith a smooth curveplot these points by joining them w ith a smooth curve
Ho w ever, you are encouraged toHo w ever, you are encouraged to learnlearn the general shapes of certain common curvesthe general shapes of certain common curves - - it's much easier than plotting points andit's much easier than plotting points andmore useful for later!more useful for later!
Allometric(rarely u sed)