11 2 TRANSFORM RECIPROCAL FUNCTIONS Effect on fx

11. 2 TRANSFORM RECIPROCAL FUNCTIONS Effect on f(x) by af(x), f(bx), f(x-c), and f(x)+d

11. 2 Vocabulary Branch _______ = Each piece of a discontinuous graph ___________ = A function that can be Rational written. Function in the form of Reciprocal ___________ = A function which belongs to Function family whose parent function Graph the Parent Reciprocal function on the TI 84 – note is

Use the TI 84 to fill in the missing parts on the next slide Hint: Type in the equations in y = and try different values

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

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

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 X=2 Y=1 : Use this for next

Graph range Find the domain and x 0 1 3 y -0. 5 -2 4 4 2. 5 Steps to graph: 1. Plot asymptotes 2. Choose 2 xvalues to the left and 2 to the right of the VA and sub into g(x) 3. Plot and connect Domain : : Range: :

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

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? Domain is integers between 1 and 52 Can’t have half a person so there will have to be 38 students to make the cost no more than $20/person