Advanced Algebra
Name:_____________________
Review Unit 10 Quiz
LT 10.01 I can use direct, inverse, and joint variation equations to model data.
LT 10.02 I can graph rational functions and identify domain, range, asymptotes, end behavior, and intercepts.
1). Write a particular function that models the following functions when x = 4, y = 5, and z = 20:
a) z varies directly with y.
b) z varies jointly with x and the square of y
c) z varies inversely with x.
d) z varies proportionately to x squared and inversely to y
2). Write an equation for the translation of y 
7
that has the given asymptotes:
x
a) x = 0 and y = 3
b) x = 5 and y = 0
c) x = - 6 and y = -1
d) x = 12 and y = 1
3). Identify the domain and range:
a) y 
5
3
x4
b) y 
2
8
x5
c)
y
4
6
x3
4). Find the domain, points of discontinuity, and x and y intercepts. Determine whether the discontinuities are
removable or non-removable.
a) y 
 x  8  x  2 
b) y 
x2
x 2  16
x4
c) y 
 x  4  x  1
x5
Domain:_________________
Domain:___________________
Domain:___________________
x-intercept(s):_____________
x-intercept(s):_______________
x-intercept(s):_______________
y-intercept:_______________
y-intercept:_________________
y-intercept:_________________
Discontinuity:_____________
Discontinuity:_______________
Discontinuity:_______________
5). Find the vertical asymptotes and any holes.
a) y 
x5
2
( x  25)( x  1)
b) y 
5
 12
x4
c) y 
3 x 2  12
x2
d) y 
12 x  5
x3  1
c) y 
4
3
x 1
6). Find the horizontal asymptotes.
a) y 
5x4  2
2x4  3
b) y 
4x  2
x2  4
c) y 
2x  7
2x  7
7). Sketch a graph. Must show vertical and horizontal asymptotes with dotted lines.
a) y 
2
 x  3 x  3
b)
y
x2
 x  4  x  2 