11.2 transform reciprocal functions effect on f(x) by af(x), f(bx), f(x-c), and f(x)+d
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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
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