Mathematics, 12.11.2019 05:31 orlandoreypot2491

A.) for this linear function, what happens to the function’s values after many iterations?
b.) are the function’s values getting close to a particular number in each case?
function : - y = (-1/2)x + 3
im just a bit confused on how to answer these questions any would be great!

A.) for this linear function, what happens to the function’s values after many iterations? b

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Answer from: eddsworldfrantic

It can be helpful to use technology (a spreadsheet program or graphing calculator) to help you with iterated functions. What you are doing is evaluating the function using its output as new input.

(A) Whenever the magnitude of the slope of a function is less than 1, it will iterate toward the point where it intersects the line y = x. Here the magnitude o the slope is 1/2, so the final value in this case will approach
.. x = y = (-1/2)x +3
.. 3/2x = 3 . . . . . . . . add x/2
.. x = 2 . . . . . . . . . . . multiply by 2/3

You can see several iterations in the table in the figure here.

(B) The values get closer to 2 in each case.

_____
Iteration of this function is like drawing a spiral on the graph. Start with some point on the function curve, such as (0, 3). Draw a horizontal line to the line y=x. this gives you x=3. Now draw a vertical line to the function curve. This will give you the point (3, f(3)) = (3, 1.5). Draw a horizontal line to y = x, repeating as many times as you like. You will see the points get closer and closer to (2, 2) with each loop around the spiral.

If the slope of the function is greater than 1, the "spiral" will diverge instead of converging.
A.) for this linear function, what happens to the function’s values after many iterations? b.) are

A.) for this linear function, what happens to the function’s values after many iterations? b.) are

Answer from: Quest

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:

Answer from: Quest

the answer would be d

straight away you can eliminate a and c because not all books contain a scientific skill because some may be fiction. c is also wrong because it saids that the only way children can learn is through books which is incorrect.

b is also wrong because reading can be a scientific skill but not always, therefore it is wrong which leaves you with d, the correct answer since it said that it can children learn.

hope this ! : 3