1. No category

Name:
__________________
Block C or H
Math 4A – Optional Rational Functions Assignment
Work is required for credit, if you need more room use a separate sheet of paper. All problems must
be completed for credit. Extra help is available after school from 2:30 – 3 on 5/26 - 5/28 and 6/1. I
will not be available for extra help on this assignment on 6/2, please plan ahead. Due date is
Wednesday, 6/3.
1.
Graph the following showing and labeling all asymptotes, holes, the y-intercept and
zeros. Be sure to give both the x and y coordinates of holes and write asymptotes as
equations. Write a limit statement for each hole, VA, and the End Behavior.
a.
y=
(x + 3)(x −1) 2
(x + 2) 2 (x −1)
€
b. y =
€
x(x + 3)(x − 4)
(x + 1) 2 (x − 4)
2. Write a formula for the graph of the function below.
6
4
2
-10
-5
5
10
-2
-4
-6
3. The rabbit population of some farm is given by the function R(t ) =
since the start of the year.
a. When is population of rabbits equal to 2000?
3000t
, where t is in months
t +1
b. As t →∞ what is the value of R (t) and what does it mean in the context of the problem?
c. What, if any, vertical asymptotes does this graph have, and what do they mean in the context of
the problem?
4.
I. Express each of the following in transformation form.
II. Identify the HA and VA.
III. Describe the transformation of g(x) and h(x) if they are transformed from f (x ) =
a) g(x ) =
€
3x + 10
x+3
b) h (x ) =
€
−2x −15
x+5
€
1
.
x
In problems 10-12, factor if needed and then find the following:
5.
f (x ) =
3x + 10
x+3



€


6.
f (x ) =
x+4
x + x −12
2



€


7.
f (x ) =
x2 − 4
x 2 + 2x


€
X-intercepts
Y-intercepts
Vertical asymptotes
Holes
End Behavior Asymptote



X-intercepts
Y-intercepts
Vertical asymptotes
Holes
End Behavior Asymptote
X-intercepts
Y-intercepts
Vertical asymptotes
Holes
End Behavior Asymptote
**** Remember asymptotes are written as equations & give the coordinates of the
intercepts and hole(s).
8. A drug is injected into a patient’s bloodstream. The concentration of the drug t hours
30t
after injection (in mg/liter) is given by the function c(t ) = 2
.
t +2
a. As t →∞ what is the value of c(t) what does it mean in the context of the problem?
Use your calculator to sketch a graph of c(t ) and answer the following:
b. What is the maximum concentration and when does it occur?
c. For what times is the concentration above 1 mg/liter?
d. When does the concentration drop below 0.5 mg/liter?
9. For the function g at the
right, state the following…
a. lim g(x )
x →∞
b. lim g(x )
x →−∞
c. lim g(x )
x →3
d. lim g(x )
x →0
e. lim g(x )
x →−2 +
10. For the function f at
the right, state the
following...
a. lim f (x )
x →3
b. lim f (x )
x →1
c. lim f (x )
x →−3
d. lim f (x)
x →2 −
e. lim f (x )
x→2 +
€
f. lim f (x )
x →2