9.2 The Reciprocal Function Family

9.2 The Reciprocal Function Family
Functions that model inverse variations belong to a family whose parent is the RECIPROCAL FUNCTION.
The general form of a family member is:
***With a single real number 'h' missing from its domain.
The value of 'a' causes the graph to stretch/shrink.
Do you remember what the values of 'h' and 'k' do?
Title: Apr 22­2:15 PM (1 of 7)
Graph the following:
**Does this graph have any horizontal or vertical asymptotes?
Title: Apr 22­2:24 PM (2 of 7)
Let's draw and compare the graphs of:
Title: Apr 22­2:28 PM (3 of 7)
Translations of Reciprocal Functions
Parent function:
Stretch (a>1)
Shrink (0<a<1)
Reflected about x­axis (a<0)
Horizontal translation by h
vertical asymptote at x=h
Vertical translation by k
horizontal asymptote at y=k Title: Apr 22­2:32 PM (4 of 7)
Sketch the graph of:
**Graph H.A.'s and V.A.'s first!
Title: Apr 22­2:41 PM (5 of 7)
Writing the Equation of a Transformation
Write an equation for the translation of that has asymptotes at and
Write an equation for the translation of that
is 4 units left and 5 units up.
Title: Apr 22­2:44 PM (6 of 7)
Page 498
#'s 1 ­ 6, 14 ­ 17, 22 ­ 24
Title: Apr 22­2:47 PM (7 of 7)