AP Calculus
1.2 Worksheet
^All work must be shown in this courseforfull credit. Unsupported answers may receive NO credit.
Piecewise Functions
1. Graph each ofthe following piecewise functions:
A-x2
b) /(*) =
, if jc< 1
fx + f ,if l<x<3
x +3
, if x > 3
2. Write a piecewise function for each function graphed below. Be sure to label each piece with the appropriate domain.
b) r
a)
-jB
^-X + ^
,
x
H 1 1
-i—i—•-4 | -|2 ;
t \ 4
;^
o^ ^
-ii
3. An earthquake that occurred at 9:17 AM cracked a water tower in a small town. Water began leaking out ofa tower at rate of 12
cm3/min for the f
irst 25 minutes, then the rate increased to 24 cmVmin for the next 30 minutes. It took 45 more minutes before the
leak was f
ixed, and in that f
inal 45 minutes, the water was leaking at a rate of 20 cmVmin. Write a piecewise function for the amount
ofwater leaking out ofthe tower Was a function oftime t. (What time should you let t = 0 represent? ^
^ II
)
'
-L i W
0
0
300
SO
)
55
100
- SS) + \oio
55 It
loo
Composite Functions
4. Suppose f(x) = x + 5 and g(x) = x2-3. Find each ofthe following:
> -f CV-3^
-" ^ (V 5")
(-3")
(LI
d) g(f(0))
- <r
~- j C^
/(/W)
'3
5. Complete the following table:
^
x2"
Vx —5
Vx2 -5
^
a)
r ^ = •^
For questions 6 and 7, f
ind / (g (x)) and determine the domain . ••
6. /-(^) = ^2+7 and g(x)= '
T
--
A
JIL
!> ,
Odd and Even Functions
8. Complete each graph assuming that the graph is (a) even and (b) odd.
a)
it—
L
9. Prove whether the following functions are even, odd,(pr>either.
-l
a) j; = 3-
c) f(x) = 2x-5x3
f >J ' t;
-f ^x)
.;
10. Write the equation ofthe following:
a) the area A of a circle as a function of its diameter d.
b) the area A ofan equilateral triangle as a function of its side length s.
AHt(^^i
c) the area A ofa rectangle as a function of its width W, where the length L is twice as long as its width W.
A = 2^x
L =
11. The cable company is asked to provide service to a customer whose house is located 2 miles f
rom the road along which the cable
is buried. The nearest connection box for the cable is located 5 miles down the road. The installation cost is $100 per mile along the
road and $140 per mile offthe road .
a) What values ofx make sense in this scenario? (This is the domain!)
b) Express the total cn.^t C of installation as a function ofthe distance x
(in miles) f
rom trie connection box to the point where the cable installation
turns offthe road.
c) Use your calculator to find the minimum possible cost ofthe installation and how far away f
rom the connection box
the cable installation should turn offthe road.
cost Q
D- (O/
12. What are the three domain issues you must remember for this course?
loq
[c
J Ao A.
t.o
r
I
v'
I A I
13. What is the domain of the ^ollowing functions?
^ ^_ l082(*-5)
b)
-i
14. Find the domain and range of the following parent functions: (write your answers in interval notation)
- (- >,w) a) li
linear
b) quadrati
c) logarithmic
| s^
V-R
e) inverse sine
d) sine
f) inverse cosine
ty f-1,0
g) inverse tangent
h) inverse linear (1/x)
i) inverse quadratic (1/x2)