Lesson 2 Shh! Please Be Discreet (Discrete)! Solidify Understanding

Ready

In problems 1–4, the work to find the slope in each representation has been started. Your job is to finish finding the slopes and show whether or not the slopes are the same for the pairs of representations provided.

1.

The first plane shows a line that passes through the points (0, -3) and (4, 5). There are dashed lines making a right triangle. x555y555000
The second plane shows a line that passess through the points (1, -1) and (2, 1). There are dashed lines making a right triangle. x555y555000

Slope =

Slope =

Is the slope the same in each? Why?

2.

In the first table, the inputs are listed as 3, 5, 9, and 12. The outputs are -19, -11, 5, and 17. >>><<<

Slope =

In the second table, the inputs are listed as 1, 2, 3, and 4. The outputs are -27, -23, -19, and -15. >>><<<

Slope =

Is the slope the same in each? Why?

3.

function 6x - 2y = 2

Slope =

function y = 3x - 6 =5

Slope =

Is the slope the same in each? Why?

4.

The first plane shows a line that passes through the points (2, 2) and (3, 2.5). dashed lines are drawn to make a right triangle. x222444y222444000
The second plane shows a line that passes through the points (2, 2) and (4, 3). Dashed lines are drawn to make a right triangle. x222444y222444000

Slope =

Slope =

Is the slope the same in each? Why?

Set

For problems 5–10, create a graphical model based on the context. Indicate if the relationship is linear or exponential and if the context is best modeled as discrete or continuous.

5.

The freeway construction crew pours of concrete in a day.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

6.

For every hour that passes, the amount of area infected by the bacteria doubles.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

7.

To meet the demands placed on them, the brick layers have started laying more bricks each day.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

8.

The average person takes in a day.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

9.

The city of Buenos Aires has been adding to its population every year.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

10.

At the headwaters of the Mississippi River, the water flows at a surface rate of .

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

For problems 11–13, a mathematical representation is provided. State whether the context it describes is discrete or continuous. Identify if it is linear (arithmetic) or exponential (geometric). Finally, create a context or story that connects with each representation.

11.

12.

Six ordered pairs are plotted on the coordinate plane: 1, 60,2, 36,3, 21.6, 4, 13 , 5, 7.8 , and (6, 4.7 ). x111222333444555666777888y101010202020303030404040505050606060707070000

13.

Go

Solve the following equations. Show your work.

Example: Solve for . . Add to both sides of the equation.

Therefore,

Example: Solve for . . Multiply both sides of the equation by .

Note that multiplying by gives the same result as dividing everything by .

14.

15.

16.

17.

Find the recursive and explicit equations for the sequences in the tables.

18.

Term

Value

19.

Term

Value

20.

Term

Value

21.

Term

Value