Question

help a teen out

Answer 1

y-intercept is just the when value given x=0, so 400 is your answer

Answer 2

not sure about the seocnd part of A

Answer 3

I guess it tells you cathy starts out with 400$?

Answer 4

hold on im reading it

Answer 5

Cathy starts out with $400. What happens to her holdings (of money) as time goes on?

Answer 6

Could you finish the following sentence, based upon the info in the table?

Cathy started out with $400. The amount of money she had by the end of each month steadily ____________ .

Answer 7

decreased

Answer 8

If you were to plot the info in the table, you could then get a rough graph by connecting the ponts you've plotted. Would this graph be that of a straight line, a parabola or some other curve? Yes, this is a decresing function.

Answer 9

striaght line @mathmale

Answer 10

How can you be sure? Every time you connect two successive points, you create a straight line segment. The overall graph is a straight line only if all of the line segments have the same slope. Connecting these points with a straight line or curve is good enough in this case to permit you to classify what kind of function you have.

Answer 11

so what are you trying to say @mathmale

Answer 12

The second half of Part A of this question asks you to explain what you can conclude about the info in the table if the y-intercept is (0,400).

One way of answering would be as follows:
"The values in this table represent the graph of a linear function with y-intercept (0,400) and slope equal to negative ... what value? ...

Answer 13

It would take just a minute to graph all of the points given in the table. That might be all you need to do to determine whether or not the data in the table represents a straight line.

Answer 14

Yup its a straight line @mathmale

Answer 15

Great. As before, I'd then conclude that the data in the table represent the graph of a straight line with y-intercept (0,400) and slope of negative something. You should find this slope.

Answer 16

what do yoiu mean?

Answer 17

how can i find the slope?

Answer 18

sorry apparently im very incompetent atm

Answer 19

Every line in the table represents a particular point.
I'd really suggest you graph all of these points.
You can find the slope of the line connecting any two points using the formula\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 20

i did graph all of them

Answer 21

for example, find the slope of the line connecting (1, 2) and (2, 4).

Answer 22

can i just use the number (0,400) and 1,320

Answer 23

(1,320)

Answer 24

\[m=\frac{ 4-2 }{ 2-1 }\]

Answer 25

i know how to find it... i just asking if those two points are valid to be used

Answer 26

What would your 1,320 represent?

Can you follow the example I gave you, above, of how to find the slope of a line segment connecting 2 points?

Answer 27

2 is the slope

Answer 28

Focusing only on the 1st two lines of the table, I get \[m=\frac{ 400-320 }{ 1-0 }=80\]

Answer 29

that gives us an answer of 80 now what?

Answer 30

The slope is "the increase in y divided by the increase in x."
As before, you answer Part A of this question by writing something like this:

"The data in the given table represent a straight line with y-intercept of (0,40) and slope of -80.

We seem to agree that the graph is uniformly decreasing; tht's why the slope is -80, not 80.

Answer 31

so i write down that for part A correct?

Answer 32

just making sure because i cannot afford an F right now

Answer 33

You're not on track to get an F; don't worry.

Yes, that's a satsifactory answer to Part A of this question.

Answer 34

hold on while i wriet it down like 1.5 minutes or less

Answer 35

@mathmale how did we get a slope of negative 80....? the numbers show positive 80

Answer 36

Start by taking the info in the top 2 lines of the given table. These points are (0,400) and (1, 320).

The slope of the line joining these two points is\[m=\frac{ 320-400 }{ 1-0 }=-80\]

Answer 37

My earlier result was wrong in that I called it 80, whereas it's -80.

Answer 38

oh i should've realized that omg

Answer 39

Part B: Important: "average value of a function on an interval" has precisely the same value as "slope" and is calculated in the same way.

Answer 40

WAIT!

Answer 41

you gave me the slope not y-intercept

Answer 42

for part A

Answer 43

hold on let me look thorugh

Answer 44

OH im so sorry i see you did tell me

Answer 45

The data in the given table represent a straight line with y-intercept of (0,40) and slope of -80. isnt the (0,40) so post to be (0,400)

Answer 46

In Part B: Imagine that you plot the points (1,320) and (3, 160).
Find the slope of the line connecting these 2 points. Your result willALSO be the "average value of the function on the interval 1 to 3.

Answer 47

Yes, I apologize. "the data in the given table represent a linear function (straight line graph) with y-intercept (0,400) and slope -80."

Answer 48

totally fine i caught it thats what counts ! :) sometimes its good when someone makes a mistake it makes the person asking the question think a bit

Answer 49

Please try now to find the slope of the line seqment connecting the points (1,320) and (3, 160).

Answer 50

You must know the slope formula by heart and know when and how to apply it.\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1}^{} }\]

Answer 51

-80

Answer 52

Hint: Your y values are 160 and 320 and your x values are 3 and 1.
Yes, the average value is -80. This represents what? Think.

Answer 53

slope

Answer 54

and y-intercept is (1,320) right?

Answer 55

In Part B you don't need or want "y-intercept." That's in Part A only.

Answer 56

(1,320) and (3,160) are two points. You are to find the average value of the function on the interval [1,3].

In other words, you are to find the slope of the line connecting the 2 points. You've alrady done that correctly; that slope is -80.

Answer 57

The most important concept here is that "average value of a function on a given interval [a,b]" has the same numerical value as the slope of the line connecting the first and second points. Again, these first and second points are (1,320) and (3,160).

Answer 58

for now you might just have to memorize that. Later, as you do more slope problems and more average value problems, you'll realize that the math is precisely the same in both.

Answer 59

okay so what do i have to do now

Answer 60

Read the question again. Ask about anything about this question that is not clear to you.

Answer 61

At least, read Part B again. What does it ask you to do? Have we done that?

Answer 62

What is the average rate of change of the function represented by the table between x = 1 to x = 3 months and what does the average rate represent?

Answer 63

okay so there is a decrease in 2 denominator

Answer 64

decrease in to months *

Answer 65

Yes. That asks you to find the "average rate of change of the function....." We've done that. What does the "ave. r. of c. " represent here? Answer: slope of the line connecting the 2 points (1,320) and (3,160).

Answer 66

are you a real professor because i'd want to attend your class (im not joking)

Answer 67

Leave the "decrease" part out.

The important thing here is that the value of the function changes from 320 to 160 as time changes from 1 to 3.

slope = (change in function value) / (change in x)

= (160-320) / (3-1) = -160/2 = -80

Answer 68

I did work 43 years as a real professor; I'm now retired.
Thank you; yours was a great compliment.

Answer 69

no i didnt inted as a copliment i implied it as you're the BEST ! as is Will.H and other but you are best out all!! (this is compliment)

Answer 70

okay i have written that down for part B

Answer 71

im pretty sure thats it right

Answer 72

Practice makes perfect; were there more time I'd encourage you to work with me on other "average value of a function" problems for the additional practice.

I do need to get off the 'Net very soon, so ask that we move on to Part C.

Answer 73

In this problem, x measures time, in months; we start with month 0, progress through months 1 aand 2 to month 3 and then stop. There is no data for months 4, 5, 6, .... .
What do you think the domain of this function is?

Answer 74

okay lets go on part C , and yes lets have some practice ... but after i ask 1 more question after this

Answer 75

Let's focus upon what you think is most important. I'd be very happy to work with you again in the future, but really need to get off the 'Net as soon as possible.
What do you know about "domain" of a function?

Answer 76

(4,80) (5,0) (6,-80)

Answer 77

alright i got you

Answer 78

I don't recognize that as the domain of the given problem (altho I do see what you are doing).

To answer the 'domain' question, you obviously have to understand what "domain" means.

Wouldn't it be silly if I asked you to find y from the table (not thru calculation) if x=-1? That would mean "1 month before this situation began."

Answer 79

Anotehr way to put it: for which x values is this function defined in the table (not by formula)?

Answer 80

Focus on the given table, focus on the given data, only.

Answer 81

OOOOOOOOOOOOOOOOOOOOOOOOOOO

Answer 82

my god

Answer 83

i see the flaw i have made

Answer 84

wait im sorry i dont

Answer 85

According to the table, this function is defined ONLY for which x values?

Answer 86

(1,-80)

Answer 87

But you've given me what looks like a point (x,y). No.
Look at the table again. Which x values are given? Make a list of them.

Answer 88

Let's put "domain" this way: "the set of input values for which the function is defined."

Answer 89

0 1 2 3 4

Answer 90

0 1 2 3 not 4

Answer 91

That's right. the function is not defined for x=1 1/2, is it?

Answer 92

Is there a y value for x=1 1/2?

Answer 93

no i dont think so

Answer 94

Correct; x = 1 1/2 is not part of the domain of this function.

Answer 95

You have listed the four x values for which the function is defined. By doing this, you have automatically written out the DOMAIN of this function.

All you have to do is to indicate that this is a set: use curly brackets: {0, 1, 2, 3}.
That's the domain of this function.

Again

Answer 96

"domain" is the set of input values for which the given function is defined.