cing mung 3/4/2024

Relations&Functions

Linear Functions

Comparing Linear and Nonlinear Functions

Analyzing and Sketching Graphs

Representations of Functions

100

Determine whether the relation is a function. Then find the domain and range.

Is the relation a function?

Responses

Domain: Select all that apply.

Responses

Range: Select all that apply.

Responses

What is

Yes

Domain; 2, 12, 13, 17

Range ; 1,11, 14, 20

100

What is the difference between a linear function and a function itself?

What is...

Linear means something that makes a line (pretty simple,) and a function is a set of coordinates or points on a graph that have only one x value to every y value. So basically, a linear function does not curve, but goes in a strait line on a graph. If it curves, this is called a non-linear function

100

Does the table represent a linear or nonlinear function?

x - 5, 6, 7, 8

y - -4, -1, 4, 11

non-linear

100

Match each graph with the situation it represents.

a. The temperature decreases quickly at first and then more slowly.

b. The temperature stays constant.

The pictures that goes with a / b

Pic 1

Pic 2

What is...

a. goes with 1

b. goes with 2

100

Determine whether the table represents a function. Then find the domain and range.

Input x: -2, - 1, -1, 1, 2.

Output y: 4, 2, 0, 2, 4.

Is the relation a function?

Yes No

Domain: Select all that apply.

-2, -1, 0, 1, 2, 4

Range: Select all that apply.

-2, -1, 0, 1, 2, 4

What is...

Domain

-2, -1, 1, 2

Range

0, 2, 4

200

Determine whether the relation is a function.

Find the domain and range.

The relation is a function

Domain; 0, 4, 8, 12

Range; -18, -9, 0, 9

200

The function y= -0.35x+0.7 represents the percent y (in decimal form) of battery power remaining x hours after you turn on a computer

A. Identify and interpret the x-intercept

B. Identify and interpret the x-intercept

What is...

A. The x-intercept is 2, which indicates that the battery has 2 hours left when you turn on the laptop.

The y-intercept is 0.7, which indicates that the battery power is at 70% when you turn on the laptop.

200

What is the definition of a non-linear function

What is...

The definition of a nonlinear function is a function that does not graph into a straight line and does not have a constant slope.

200

How do you analyze a sketching graph?

What is...

You look for key terms like " decrease " "increase " constant " and check for the graph to see if it fits with the graph. After finding out how the graph is represented with the words you form them in to a sentence

200

Determine whether the table represents a function. Then find the domain and range.

Is the relation a function?

Yes No

Domain: Select all that apply.

-2, -1, 0, 1, 2, 4

Range: Select all that apply.

-4, -3, -2, -1, 0, 1

What is...

Yes, the relation is a function

Domain

-2, -1, 0, 1, 2

Range

-4, -3, -2, -1

300

Determine whether the relation is a function. The find the domain and range.

(-9,0), (-2,5), (5,10), (12,10)

What is

Yes, the relation is a function because each input has exactly one output. So, the relation is a function.

The domain is -9, -2, 5, 12.

The range is 0, 5, 10, 10.

300

The table shows the height y (in a thousand feet) of an unmanned aerial vehicle (UAV) x minutes after it begins its descent from cruising altitude.

Minutes x : 0, 10, 20, 30

Height (thousand of feet) y : 52, 48, 44, 40

Write a linear function that relates y to x. Interpret the slope and y-intercept.

y= ????

FILL IN THE BLANKS

The slope indicates that the height ______ feet per minute. The y-intercept _______ indicates that the descent ______at a cruising altitude of ______

What is...

y= -2x/5 +52

1. decreases 400

2. begins

3. 52,000

300

What is the definition of a linear function?

What is...

Linear functions graph into a straight line

300

As you snowboard down a hill, you gain speed at a constant rate. You come to a steep section of the hill and gain speed at a greater constant rate. You then slow down at a constant rate until you come to a stop. Choose the graph that represents this situation.

GRAPH A:

GRAPH B:

GRAPH C:

GRAPH D:

What is...

The graph is A

300

Determine whether the graph represents a function.

The relation ____ a function

Find the domain and range.

This graph does NOT represent a function.

Domain

-1< x and x < 3

Range

-2 < y and y < 2

400

Describe how relations and functions are different.

What is

A relation pairs inputs with outputs. A function is a relation that pairs each input with exactly one output.

400

The function y=0.15x+0.3 represents the percent y (in decimal form) of battery power remaining x hours after you plug in a laptop computer. Identify and interpret the slope.

What is...

The slope is 0.15. This means that the power increases by 15% per hour

400

Which equations represent nonlinear functions?

1. y= 9(x+1)

2. y= 3x+4

3. y= x (by the power of 2) + 8

4. y= x(by the power of 2) - 8

What is...

3 and 4

3. y= x (by the power of 2) + 8

4. y= x(by the power of 2) - 8

400

Two rowing teams are in a race. The graph shows their distances from the finish line over time. Describe the speed of each team throughout the race.

Determine which team finishes first.

Team ___ finishes first

What is...

Team A starts at the same place as B and then it smoothy goes down in a constant rate although it is slow. Then when it reaches to a certain point they go downhill straight. Team B is going up before A and then they go down hill before A does but then they stop and turn away from the original place.

Team A

400

Do you think this graph is a linear function or not?

Yes, this graph is a linear function because every possible vertical line intersects the graph in one or less points.

Something like this

or something like this

500

Select the ordered pairs shown in the mapping diagram.

OPTIONS TO PICK

(-1, 4), (0,-5), (2,-3)

(3, -2), (2,3), (-3,2)

(0, 4), (-5,0),

Determine whether the relation is a function.

Find the domain and range.

What is

(1,-4)

(3,2)

(0, -4)

(0, -5)

(2, -3)

No, the relation is NOT a function

Domain; 0,1,2,3

Range; -5, -4, -3, -2

500

Two arcades charge an entrance fee and a fee per game. At Arcade A, the total cost y (in dollars) of playing x games represented by the linear function y=0.25x+1.The table shows the total cost for playing x games at Arcade B. Determine which arcade is described by each phrase below.

Number of Games x ; 0, 4, 8, 12

Total Cost (dollars) y ;

What is...

Arcade 1: No correct answer

Arcade 2: higher total cost for 12 games

higher entrance fee

500

Which equations represent linear functions?

1. 5x+ 4y= -5

2. 5x+ 4y= -3

3. y= 3x-1

4. y = -6/x

What is...

1. 5x+ 4y= -5

2. 5x+ 4y= -3

3. y= 3x-1

500

Dig Deeper

The graph shows your speed during a run. Choose the part of the graph that describes when you slow down at a constant rate.

1.A

2.B

3.C

4.D

What is...

500

Determine whether the table represents a function.

Input x: -1, 0, 1, 1, 2.

Output y: -2, -1, 0, 1, 2.

The table ____ a function

Find the domain and range.

DOMAIN: ?

RANGE: ?

The table is NOT a function

Domain:

-1, 0, 1, 2

Range:

-2, -1, 0, 1, 2