Advanced Algebra Name: ________________________________ Unit 10 Quiz Review 3/19/14 Learning Targets: 10.01 I can use direct, inverse, and joint variation equations to model data. 10.02 I can graph rational functions and identify domain, range, asymptotes, end behavior, and intercepts. Material: 1. Direct, inverse and joint variation equations: a. Use data to find k-­‐value. Then find new data. 2. Reciprocal functions: a. Shifting a parent function to have new asymptotes (give an equation) b. Name asymptotes, domain and range of a function 3. Rational functions: a. Find: discontinuities (and their type), domain, range, intercepts, asymptotes b. Sketch a graph REVIEW: 1. Suppose x and y vary inversely, and y=6 when x=9. What is the value of y if x = 3? 2. Variable z varies directly with x and inversely with y. When x=12 and y=4, z=9. What is the general function that models this data? 3. What is the k value if y varies jointly with x and z and y=120 when x=8 and z=5? !
4. Describe the shifts from the parent graph of 𝑦 = ! . What are the vertical and horizontal asymptotes of each function? !
!
a. 𝑦 = (!!!) + 4 b. 𝑦 = (!!!) − 5 !
5. Write the equation for the translation of 𝑦 = ! that has the following asymptotes. Also, give the domain and the range for each function. a. 𝑦 = −8, 𝑥 = 4 b. 𝑦 = 3, 𝑥 = 6 6. For each of the following functions, find the domain, points of discontinuity, and x-­‐ and y-­‐ intercepts. Tell whether each discontinuity is removable or non-­‐removable. a. 𝑦 =
(! ! !!")
(!!!)
Discontinuity:_____________
(!!!)(!!!)
b. 𝑦 = (!!!)(!!!) Discontinuity:_______________
Domain:_________________
Domain:___________________
x-intercept(s):_____________
x-intercept(s):_______________
y-intercept:_______________
y-intercept:_________________ 7. Find the horizontal asymptote:
a. 𝑦 =
!! ! !!
! ! !!
!!!!
b. 𝑦 = ! ! !!"
8. For these functions, tell where the graph has holes or vertical asymptotes. a. 𝑦 =
! ! !!!!
!!!
!!!!
b. 𝑦 = (!!!)(!!!) 9. Graph the following functions. Be sure to label horizontal and vertical asymptotes with dotted lines. !
!
a. 𝑦 = !!! − 1 b. 𝑦 = ! ! !!!!!"