Re-Introduction to Functions

8/7/2019 Re-Introduction to Functions

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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)

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Re-Introduction to Functions