At the beginning of the semester students reported that they spend an average of 5 hours per day watching television, decreasing at an average rate of 30 minutes per week. professors reported that they spend an average of 1 hour per day watching television, increasing at an average rate of 30 minutes per week. (source: blitzer: thinking mathematically, 2019) a. write a function, s, for the amount of time students watch television during week, x. b. write a function, p, for the amount of time professors watch television during week, x. c. by which week do students and professors both watch the same number of hours of television? how many hours?

After 29 week both watch 21 hours of television per week.

Step-by-step explanation:

Consider the provided information.

Part (A)  

It is given that At the beginning of the semester students reported that they spend an average of 5 hours per day watching television

That means they spent 5×7 = 35 hours in first week.

Then decreasing at an average rate of 30 minutes per week.

In week 2, it will be 34.5 hours per week.

In 3rd week, it will be 34 hours per week and so on.

For x weeks the required equation will be:

S = 35 - 0.5(x-1)

S = 35.5 - 0.5x

Part (B)

Professors spends 1 hour per day in a week he spent 1×7=7 hours.

For 2nd week, it will be 7.5 hours per week.

For 3rd week, it will be 8 hours per week and so on.

For x weeks the required equation will be:

P = 7 + 0.5(x-1)

P = 6.5 + 0.5x

Part (C)  

Equate the equations

35.5 - 0.5x = 6.5 + 0.5x

0.5x + 0.5x  = 35.5 - 6.5

x  = 29

Now substitute x=29 in P= 6.5 + 0.5x

P = 6.5 + 0.5(29)

P = 6.5 + 14.5

P = 21

Thus, after 29 week both watch 21 hours of television per week.

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: