082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

58 Chapter 2 Engineering functions
Solution (a) y(t +2) = (t +2) 2 + (t +2) =t 2 +5t+6
( ( ) t t 2 ( t
(b) y = + =
2)
2 2)
t2 4 + t 2
2.3.2 Graphofafunction
A function may be represented in graphical form. The function f (x) = 2x is shown in
Figure2.4.Notethatthefunctionvaluesareplottedverticallyandthexvalueshorizontally.Thehorizontalaxisisthencalledthexaxis.Theverticalaxisiscommonlyreferred
toastheyaxis, sothat weoften write
y=f(x)=2x
f (x)
2
–2
1 x
Sincexandycan have a number of possible values, they are called variables:xis the
independent variable and y is the dependent variable. Knowing a value of the independent
variable,x, allows us to calculate the corresponding value of the dependent
variable,y. To show this dependence we often writey(x). The set of values thatxis allowedtotakeiscalledthedomainofthefunction.Adomainisoftenanintervalonthe
x axis. For example, if
–4
Figure2.4
Thefunction: f (x) = 2x.
f(x)=3x+1 −5x10 (2.1)
thedomainofthefunction, f,istheclosedinterval[−5,10].Ifthedomainofafunction
isnot explicitly given itis taken tobe the largestset possible. For example,
g(x)=x 2 −4 (2.2)
hasadomainof (−∞,∞)sincegisdefinedforeveryvalueofxandthedomainhasnot
been given otherwise. The set of values that the function takes on is called the range.
The range of f (x) in Equation (2.1) is [−14,31]; the range ofg(x) in Equation (2.2) is
[−4,∞).
Wenowconsiderplottingthefunction f (t) =t 2 for0 t < 100inatechnicalcomputing
language. Firstwegenerate a number set as shown inSection 2.2.
t= 0:1:100
Then we produce a graph of the function by using the MATLAB ® plot command to
give the following
plot(t, t.^2)
Example2.4 Consider the function, f,given by the rule:‘squarethe input’. This can bewritten as
f(x)=x 2
Theruleandthegraphof f areshowninFigure2.5.Thedomainof f is (−∞,∞)and
the range is[0,∞).