# Need help making the graph for price change in this question

Algebra

### Need help making the graph for price change in this question

Lines can be used to approximate a wide variety of functions; often a function can be described using many lines.

If a stock price goes from \$10 to \$12 from January 1st to January 31, from \$12 to \$9 from February 1st to February 28th, and from \$9 to \$15 from March 1st to March 31th is the price change from \$10 to \$15 a straight line?

It is clear that in each of the three time intervals mentioned there was a complex daily variation of prices as in an electrocardiogram. But what would be a simplified solution for a first naive view of the situation? Would a simple function hold up? What is the simplest function to represent this situation? Does your naïve initial and simplified model allow you to predict the behavior of the stock in the next month?

How can I use three “pieces” of lines to describe the price movements from the beginning of January to the end of March? Show the graph for the price movement.

THE URGENT PART:: Write your equations following the example (which will be put into 'desmos' online graphs)

y = x + 2 {0 < x < 2}

y = –x + 6 {2 < x < 5}

y = 2x – 9 {5 < x < 8}
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### Re: Need help making the graph for price change in this ques

No, the stock price is NOT a straight line because a straight line always goes in the "same direction". Here, the stock price is going up in January and down in February.

ASSUMING the price is linear in each month then the graph is a "broken line" with a different line segment for each month.
Taking "t" to be the number of days since Jan. 1 and "P" to be the stock price, P= (12-10)t/31+ 10= (2/31)t+ 10 for January.

For February, since the stock price goes form 12 down to 9 over 28 days,
P= (9- 12)(t- 31)/28+ 12= -(3/28)t+ 93/28+ 12= -(3/28)t+ 429/28.
(The "t- 31" is since Feb 1 is the 32 day since Jan 1.)

For March, since the stock price goes from 9 to 15 in 31 days,
P= (15- 9)(t- 59)/31+ 9= (6/31)t- 354/31+ 9= (6/31)t- 279/31.

Following the example given, that can be written
P(t)= (2/31)t+ 10 {0< t< 32}
P(t)= -(3/28)t+ 429/28 {31< t< 60}
P(t)= (6/31)t- 279/31 {59< t< 90}

HallsofIvy

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