Worksheet – 3.7
Name_________________________________
1. Find the domain for each of the following functions. In part c., assume A and B are constants.
____________a. T (m) 
___________b. f (t ) 
m2  4
m  2(m  3)
15t 3  5t 2  3t  2
4t 2  12
____________c. g (r ) 
r 6
Ar  B
y2  5
__________d. h( y )  3
y  5y2  6y
2. Create an equation for
a. A rational function (not a polynomial) with no vertical asymptotes.
b. A rational function with asymptotes y  0 , x  2 , x  3
1
c. A rational function with asymptotes y   , x  4 , x  6 and zeros at 2 and 7
3
d. A rational function with asymptotes y 
6
, x  6 , x  3 and zero at 1 only
5
3. Use the graphs of f (x) and g (x ) given below to answer the following:
a. If we let h( x) 
f ( x)
, is h(x) a rational function? Why?
g ( x)
b. What is (are) the vertical asymptotes of h(x) ?
c. What is (are) the zeros of h(x) ?
4. Create an equation for each:
a. The graph of y 
1
shifted two units to the right.
x 1
b. The graph of y 
1
shifted three units down, then reflected across the x-axis.
x
2
5. Suppose y  f ( x) is a rational function with a horizontal asymptote of y  3 and a vertical
asymptote of x  5 . Suppose this function has no other asymptotes.
a. What is the domain of f (x) ?
b. What are the asymptotes of the transformed function y  f x  1 ?
c. What are the asymptotes of the transformed function y  f ( x)  2 ?