Exercise #1: Jannine has $450 in her savings account at the beginning of the year. She places money in the account at the rate of $5 per week. We want to model the amount of money she has in savings, s, as a function
of the number of weeks she has been saving, w.
(a) Fill out the table below for some of the number of (b) Use information in the givens or in the table to
weeks. Show the calculations that result in your write an equation for the savings, s, as a linear
answer.
function of the weeks she has been saving, w.
Number
Amount in
Calculation
of weeks, w
Savings, s
0
1
(c) If Jannine saves for exactly one year, what is the
range in her savings over the year? Show how
you arrived at your answer.
5
10
(d) Why would it not make sense to evaluate s(6.5)? In other words, what types of numbers belong in the
domain of this linear function?
(e) Use two points from the table to verify that the rate of change of the function is 5. How do the units show
up in the calculation?

this is answer of 144 cubic meters

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

there still no table