4-5 Writing a Function Rule
Quick Review
To write a function rule describing a real-w orld situation, it
is often helpful to start w ith a verbal m odel of the situation.Ex e r c i se s
Write a function rule to represent each situation.- Landscaping The volume Vrrem ainingina243-ft3
Ex a m p l e
At a bicycle motocross (BMX) track, you pay $40 for a
racing license plus $15 per race. What is a function rule
that represents your total cost?
total cost = license fee + fee p er race • n u m b e r of races
C = 40 + 15 r
A function rule is C = 40 + 15 • r.pile of gravel d ecreases by 0.2 ft3 w ith each shovelful
s of gravel spread in a walkway.- Design Your total cost C for hiring a garden designer
is $200 for an initial consultation plus $45 for each
hour h th e designer spends draw ing plans.
4-6 Form alizing Relations and Functions
Quick Review
A relation pairs n u m b ers in th e domain w ith n u m b ers in
the range. A relation m ay or m ay n o t be a function.Ex e r c i s e s
Tell whether each relation is a function.- { ( - 1 , 7), (9, 4), (3, - 2 ) , (5, 3), (9, 1)}
Ex a m p l e
Is the relation { ( 0 ,1), (3,3), (4,4), (0,0)} a function?
The x-values of th e ordered pairs form the dom ain, an d the
y-values form th e range. The dom ain value 0 is p aired with
two range values, 1 an d 0. So th e relation is n o t a function.- {(2, 5), (3, 5), (4, - 4 ) , (5, - 4 ) , (6, 8)}
Evaluate each function for x = 2 and x = 7.
21. f{x) = 2x — 8 22. h(x) = — 4x + 61- The dom ain of t(x) = - 3 .8 x - 4.2 is { - 3 , -1 .4 , 0, 8}.
W hat is th e range?
4-7 Arithmetic Sequences
Quick Review
A sequence is an o rdered list of num bers, called term s, that
often form s a pattern. A seq u en ce can be re p resen te d by a
recursive form ula or an explicit form ula.Ex a m p l e
Tell whether the sequence is arithmetic.
5, 2, - 1 , -4,...-3 - 3The s eq ue nce has a
common difference of- 3 , so it is a rith m e tic.
Ex e r c i s e s
For each sequence, write a recursive and an explicit
formula.- 3,8,13,18, ...
- 4, 6.5, 9, 11.5,...
25. -2, -5, -8, -11, ...
27. 18,11,4, -3 ,. ..
For each recursive formula, find an explicit formula that
represents the same sequence. - A{ n) = A{ n — 1) + 3; A ( l ) = 4
- A[ r i ) = A{ n — 1 ) + 11; A ( l ) = 13
- A{ n) = A{ n - 1) - 1; A(l) = 19
286 Ch ap t er 4 Ch ap t er Rev i e w