Warmup
1. Determine the number of horizontal and vertical asymptotes for f  x 
A
B
C
D
0
1
2
3
3
.
x  3x
2
2. If y varies jointly as m and p and inversely as the cube root of w. If
y = 12, when m = 3, p = 2, and w = 512, find y when m = 5, p = 2, and
w = 125.
3.
4) What are the asymptotes for the function
?
5) List vertical asymptote, horizontal asymptote and x and y intercept for each given function.
Decide which function matches the graph?
VA
HA
X intercept
Y intercept
Classwork Review 8.1-8.3
1. Determine whether x. and y show direct variation, inverse variation, or neither. Write the model
relating the variables.
5
8
15
x 2
2
3
4
x 1
y
1
4
9
y
16
60
24
15
8
2. z directly proportional to the x and inversely proportional to the square of y ___________________
3. If x and y vary directly and x = 3 when y = 12.
 Write the model relating the variables: ________________
 When x= -5, y= _________
4. If x and y vary inversely and x = 2 when y = 18
 Write the model relating the variables: ________________
 When x= -3, y= _________
5. Explain what is rational expression: ___________________________________________________
6. How do you find x-intercept? ________________________________________________________
7. How do you find y-intercept? _______________________________________________________
8. How do you find domain of rational functions? __________________________________________
9. How do you find range of rational functions? ____________________________________________
Graph the following function. Show ordered pairs in a table, and fill in the information about
asymptotes, intercepts, domain, and range.
4
5
10. f ( x) 
x 1
x
y
x-intercept(s):__________________
y-intercept:__________
Vertical Asymptote(s):__________________
Horizontal Asymptote:___________
Domain:_____________________________
Range:________________________
Graph the following functions. Show ordered pairs in a table, and fill in the information about
asymptotes, intercepts, domain, and range.
3x  6
11. g ( x) 
x4
x
y
x-intercept(s):__________________
y-intercept:____________________
Vertical Asymptote(s):__________________
Horizontal Asymptote:___________
Domain:_____________________________
Range:________________________
2 x2  6 x  8
12. h( x)  2
x  x6
x
y
x-intercept(s):__________________
y-intercept:____________________
Vertical Asymptote(s):__________________
Horizontal Asymptote:___________
Domain:_____________________________
Range:________________________