1. 11.2 Transform Reciprocal FUnctions
Effect on f(x) by af(x), f(bx), f(x-c), and f(x)+d

2. 11.2 Vocabulary Branch Rational Function Reciprocal Function
______________ = Each piece of a discontinuous graph
Rational Function
_____________________ = A function that can be written
in the form of
Reciprocal Function
_____________________ = A function which belongs to
family whose parent function is
Graph the Parent Reciprocal function on the TI84 – note asymptotes !

3. Use the TI84 to fill in the missing parts on the next slide
Hint: Type in the equations in y = and try different values

4. Investigate Transformations of
Given describe the SPECIFIC effect of a,b,c, and d :
Equation
Effect
Be more SPECIFIC
Vertical stretch, compress, or reflect
Horizontal stretch, compress, or reflect
Horizontal Translation
Vertical Translation
Vertical stretch
Vertical compress
Reflect across x-axis
Horizontal stretch
Horizontal compress
Reflect across y-axis
Shift right
Shift left
Shift up
Shift down
Does a, b, c, or d cause the asymptotes to move off the x & y axes?

5. Graph Find the domain and range in interval notation
“c” and “d” are “0”
so the x-y axes are the asymptotes
Domain:
Range: x y -3 -1 1 3
Fab-5 works but I chose friendlier numbers to sub in -1 -3
und
a=3 so this
caused a vertical stretch 3 1
Graph the fcn on the calculator but change 3 to “-3” Discuss.

6. Identify effects of a, c, and d from f(x) to g(x)
Compare
Identify effects of a, c, and d from f(x) to g(x) a=
3 there is a vertical stretch by factor of 3 c=
2 shift right 2 so asymptote moves right 2 d=
1 shift up 1 so asymptote moves up 1
Write the equations of the asymptotes of g(x)
Horizontal asymptote:
Vertical asymptote:
Y =1
X = 2
Use this for next slide

7. Graph Find the domain and range
Steps to graph:
1. Plot asymptotes
Choose 2 x-values to the left and 2 to the right of the VA and sub into g(x)
Plot and connect x y 1 3 4
Domain::
-0.5 -2
Range:: 4
2.5

8. Write an equation for the transformation of given:
a=– 2 c = 3 d = – 4
HA = – VA = 5
Identify the domain and range in set notation

9. The rowing club is renting a 57-passenger bus for a day trip
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?
How many students must ride the bus to make the cost per student no more than $20?
Solve as if this was an equation
The cost C per student depends on the number of students n attending.
So, what is the domain of the function?
Can’t have half a person so there will have to be 38 students to make the cost no more than $20/person
Domain is
integers between 1 and 52