Precalculus Bc/ap Calculus Ab Summer Assignment Worksheet Page 2
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49) You need a Lear jet for one day. Knowing that Swissair rents a Lear jet with a pilot for $2000 per day plus $1.75
per mile and that Air France rents a Lear jet with a pilot for $1500 per day plus $2.00 a mile, find the following:
a) For each company, write a formula for cost as a function of distance traveled.
b) Sketch graphs of these functions, labeling intercepts and point of intersection.
c) If cost were the only issue, when would you rent from Air France? Why or why not?
x 3y 1
10) Find the line that passes through the point (-1,3) and the point of intersection of the lines
and
2x y
5
. Leave your answer in point slope form,
.
III. Function Basics (No calculator)
11) Sketch a graph and identify the domain and range of the following:
2
4 x ,
5 x
1
3
3
f (x)
x
,
1 x
3
g(x)
2[2x] 1
a)
b)
2
2
x
3,
3 x
10
x
h(x)
2 5 4
x
f (x)
c)
d)
2
x
1
12) Identify the parent function and describe with translations and dilations how each graph can be obtained from that
parent function.
1
x
3
:
f (x)
x , g(x)
,
h(x)
x ,
k(x) log x,
m(x) 2 , g(x) x
Parent functions
x
7
3
y
.5(x 4)
2
y
x 2 1
y
3
a)
b)
c)
x
1
5
(1 x)
y
3
x
4
y
2 log (x
3)
5
y 2
3
d)
e)
f)
2
1
2
f (x)
f (x)
(x
3)
x
3
13) Find
, the inverse of
when
. Graph both functions on the plane and
1
1
f (f
x ) x
f (f x ) x
analytically show
and
.
14) Given the following graph of f(x):
Sketch a graph of the following functions. Use a separate graph for each one.
a) f(x) + 2
b) -f(x) + 1
c) -f(x+3)
d) 3 f(x-2) +1
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