MatInd I 2-Function Graphs

7/26/2019 MatInd I 2-Function Graphs

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Basic

Mathematics TIP-FTP-UB

By Azimmatul Ihwah



Functions GraphsBasic Mathematics

TIP-UB



Graph of Linear function

• Common form : y = f(x) = ax + b

where, a and b is constants

a = slope / gradient

b = intersect point at y-axis

• The graph :



Graph of Linear function

• xample : !"etch the graph of y = #x + $

!ol%tion &ntersection point with x-axis '

&ntersection point with y-axis '



Graph of rational function•

raph of rational f%nction from y = (ax + b)/(cx + d) is a hyperbole with,ertical asymtot at x = * d/c

horiontal asymtot at y = a/c

• !teps to draw a rational f%nction graph :

!tep : draw the asymtot

!tep # : plot two dots to each side of ertical asymtot

!tep : connect two dots in the right and left of asymtot

xample :

•



Graph of ua!ratic function

• Common e.%ation of a .%adratic f%nction is y = ax# + bx + c

• raph of .%adratic f%nction is a parabolic graph, co%ld be facing %p

or down

0acing %p ertex is at the lowest point (slope)

0acing down ertex is at the highest point (pea")

y = ax# + bx + c

facing %p if : a is positie

facing down if : a is negatie




• Symmetrical Line

• 1 parabole has a symmetrical line at the middle that c%ts the hyperbole into

two symmetrical sides always crosses ertex 2

•&f the .%adratic f%nction e.%ation is y = ax# + bx + c, the symmetrical linee.%ation denoted as :

•

xample :0ind the symmetrical line from e.%ation

y = x# + 3x + 4 '




• Determining vertex

• !ymmetrical line is always crossing ertex can determine the x-

axis coordinate of the symmetrical line

• xample :

0ind the ertec coordinates from e.%ation

y = -#x# + 3x * '

x = # y = -#(#)# + 3(#) *

= -3 + $ *

y = 5

6ertex (#,5)




• Drawing a parabole

• !tep : find the symmetrical line

• !tep # : find the ertex

• !tep : find another two dots, reflects them %sing symmetrical line

• !tep 7 : connect all fie dots to form a hyperbole

• xample :

8raw a graph from the e.%ation

y = #x# * 7x * 2



"#ponential function

• Exponential function

• xponential f%nction is defined as :

f(x) = ax

where a 9 , a ; , and x is any real n%mber

• xample : f(x) = #x

x f ( x ) ( x , f ( x ))

-2 ¼ (-2, ¼)

-1 ½ (-1, ½)

0 1 (0, 1)

1 2 (1, 2)

2 4 (2, 4)





• 8omain and <ange '

raph of f(x) = ax, a 9 raph of f(x) = ax, a





• 0rom the earlier e.%ation of f(x) = #x, draw :

a f(x) = #x *

b f(x) = #-x



Graph of lo$arithmic function

• >ogarithmic f%nction with basis a where a 9 and a ; is defined as :

• ?hen conerting an exponential form into a logarithmic form, ma"e

s%re that both forms are e.%ally conerted

xamples : Log2 16 = 4 Log4 1 = 0

Log3 1/9 = -2 Log3 31/2 = ½




• Exponential vs Logarithmic




• Exponential vs Logarithmic



Graph of a%solute &alue function

• 1bsol%te al%e f%nction :

- is a linear e.%ation

- 6-shaped graph

- graph ma"ing is similar to the graph of linear e.%ation

- has a ertex 2 different from linear f%nction

- common form : y = @x * b@ + c , where b and c are real n%mbers



Graph of a%solute &alue function

• xample :

8raw a graph from y = @x + @ * #

• !ol%tion :

- find the ertex coordinate : (b, c)

- find the other al%es of x and y to draw a graph



Graph of tri$onometry function

• raph of sin f%nction

• raph of cos f%nction

x 0 /2 3 /

2

2

Sin x 0 1 0 -1 0

x 0

/2

3

/2

2

Cos x 1 0 -1 0 1



Graph of tri$onometry function

• Examples

!"etch the graph of y = #sin (* x)

Solution :

<ewrite the f%nction into the form of y = a sin bx with b 9

%na"an sifat trigonometri sin (* x) = * sin x

y = #sin (* x) = * #sin x

1mplit%do : @a@ = @ *#@ = #

Aeriode : #π/b = #π/

x 0 /6 /3 /2 2 /

3

y = -2 sin

3x

1 -2 0 2 0



Graph of functions %elow

8raw the graph

y = #x-

# y = -#x# + x *

y = #-x *

7 y =5 y = @x+#@ - 5

•

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MatInd I 2-Function Graphs