Jacob has 69 flowers for a big party decoration. In addition, he is planning to buy some flower arrangements that have 16 flowers
each. All of the arrangements cost the same. Jacob is not sure yet
about the number of flower arrangements he wants to buy, but
he has enough money to buy up to 5 of them. Write a function to
describe how many flowers Jacob can buy. Let x represents the
number of flower arrangements Jacob buys. Find a reasonable
domain and range for the function.

The function is 16x + 69

Domain of the function is [0, 5]

Range of the function is [69, 149]

Step-by-step explanation:

Given - Jacob has 69 flowers for a big party decoration. In addition, he is

planning to buy some flower arrangements that have 16 flowers

each. All of the arrangements cost the same. Jacob is not sure yet

about the number of flower arrangements he wants to buy, but

he has enough money to buy up to 5 of them.

To find - Write a function to  describe how many flowers Jacob can buy.

               Find a reasonable  domain and range for the function.

Proof -

Let us assume that,

The  number of flower arrangements Jacob buys = x

Given that,

Each Flower arrangement have 16 flowers.

So,

x Flower arrangements have 16x flowers.

Also given that, Jacob has 69 flowers for a big party decoration.

So,

Total flowers Jacob can buy, y = 16x + 69

So,

The function is 16x + 69

Now,

Given that, Jacob can buy up to 5 flower arrangements

i.e. x ≤  5

So,

Domain of the function is [0, 5]

Now,

When x = 0

y = 16(0) + 69 = 69

When x = 5

y = 16(5) + 69 = 149

So,

Range of the function is [69, 149]

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:

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~