11.2 TRANSFORM

RECIPROCAL

FUNCTIONS

Effect on f(x) by af(x), f(bx), f(x-c), and f(x)+d

11.2 Vocabulary

______________ = Each piece of a discontinuous graph

_____________________ = A function that can be written in the form of )(

)(

xQ

xP

_____________________ = A function which belongs to family whose parent function is

01

xwherex

y

Branch

Rational Function

Reciprocal Function

Graph the Parent Reciprocal function on the TI84 – note asymptotes !

Hint: Type in the equations in y = and try different values

Use the TI84 to fill in the missing parts on the next slide

Click icon to add picture

Investigate Transformations of x

y1

Given describe the SPECIFIC effect of a,b,c, and d :

xxf

1)(

Equation Effect Be more SPECIFIC

Vertical stretch, compress, or

reflect

Horizontal stretch, compress, or

reflect

Horizontal Translation

Vertical Translation

)(xfa

)(bxf

)( cxf

dxf )(

0

10

1

a

a

a

0

10

1

b

b

b

0

0

c

c

0

0

d

d

Does a, b, c, or d cause the asymptotes to move off the x & y axes?

Vertical stretch

Vertical compressReflect across

x-axis Horizontal stretch

Horizontal compress

Reflect across y-axis Shift right

Shift leftShift up

Shift down

Graph Find the domain and range in interval notation

x y

-3

-1

0

1

3

-1

-3

und3

1

“c” and “d” are “0”

so the x-y axes are the

asymptotes

xy

3

Fab-5 works but I chose

friendlier numbers to sub in

Domain:

Range:

,00,

,00,

a=3 so this caused a vertical

stretchGraph the fcn on the calculator but change 3 to “-3” Discuss.

Compare 12

3)(

1)(

x

xgtox

xf

Write the equations of the asymptotes of g(x)

3 there is a vertical stretch by factor of 3

a=

c=2 shift right 2 so asymptote moves right 2

d=1 shift up 1 so asymptote moves up 1

Identify effects of a, c, and d from f(x) to g(x)

Horizontal asymptote:

Vertical asymptote:

X=2 Y=1Use this for next slide

Graph Find the domain and range

12

3)(

x

xg

Steps to graph:1. Plot asymptotes2. Choose 2 x-

values to the left and 2 to the right of the VA and sub into g(x)

3. Plot and connect

x y

0

1

3

4

-0.5-24

2.5

Domain::

Range::

,22,

,11,

Write an equation for the transformation of given: x

xf1

)(

a=– 2 c = 3 d = – 4

HA = – 2 VA = 5

43

2

x

y 52

1

x

y

Identify the domain and range in set notation

4/:

3/:

yyrange

xxdomain 5/:

2/:

yyrange

xxdomain

The rowing club is renting a 57-passenger bus for a day trip. The cost of the bus is $750. Five

passengers will be chaperones.

If the students who attend share the bus cost equally, what function models the cost per student C with respect to the number of students n who attend?

nc750

The cost C per student depends on the number of

students n attending.So, what is the domain of

the function?students

meanschaperonespassengers

max52

557

Domain is integers between 1 and 52

How many students must ride the bus to make the cost per student no more than $20?

20750

n

75020 n

Solve as if this was an equation

5.37nCan’t have half a person so there will have to be 38 students to make the cost no more than $20/person