Show:
6.1
6.2
6.3
6.4
Challenge problems
100
The input in an ordered pair
What is input?
100
Identify the input and the output variable for the function rule of y=2x+5
What is input variable:x

output:y?

100
Is y=mx+b a linear function when b=0
What is yes?
100
Describe how linear functions are different from nonlinear functions.
What is a linear function has a constant rate of change. A nonlinear function does not have a constant rate of change?
100
The output is half the input


The output is three less than the input

What is 

y=1/2x

y=x-3?

200
Each input has one output


True or False

What is true?
200
write an equation that describes the function

input,x       output,y 

1               8

2               9

3               10

4               11

What is y=x+7?
200
Use the table to write a linear function that relates y to x


x  -8  -4  0  4

y  2   1   0  -1


What is y=-1/4x?
200

Does the table represent a nonlinear or linear function

x  5  11  17  23

y  7  11  15  19

What is linear function?
200

Describe the pattern in the mapping diagram. Then complete the diagram.

1   -3

2    2

3    7

4   

5

6

What is as each input increases by 1, the output increases by 5?
300

Determine if function with given pairs.

(-3,7) (0,14) (-2,7) (-1,14)

What is yes?
300
Find y

y=x+5  x=3

y=1-2x  x=9

y=2x cubed  x=3

what is 

y=8

y=-17

y=54?

300
number of movies,x  0  1  2  4

cost,y                      0  3  6  12

write a linear function that relates y to x

What is y=3x?
300

Daily Double

The table show the volume V (in cubic feet) of a cube with an edge length of x feet. Does the table represent a linear or nonlinear function.

Edge, Length,x  1  2  3    4    5       6      7       8

Volume,V          1  8  27   64  125  216  343  512

Volume,V          1  8  27  64

Volume, V         1

What is nonlinear?
300

Daily Double

The frequency y (in terahertz) of a light wave is a function of its wavelength (in nanometers). Does the table a nonlinear or linear function?


color                 red   yellow  green  blue  violet 

wavelength,x    660     595     530    465   400

frequency,y      454     504     566    645   749

 What is nonlinear; As x decreases by 65, y increases by different amounts?

400
Describe the pattern of the inputs and output with the given pairs.


(9,5) (6,15) (3,25) (0,35)

What is as each input increases by 3, the output decreases by 10?
400

You decide to make and sell bracelets. The cost of your materials is $84. You charge $3.50 for each bracelet. 

Write a function that represents the profit p for selling b bracelets.

What is p=3.50b-84?
400
Can a graph of a linear function be a horizontal line? explain
What is yes, a horizontal line is a nonvertical line?
400

Make a graph with these coorindate points. Then decide if the graph is linear or nonlinear.

1. (0,4) (1,8) (2,12) (3,16)

2. (6,21) (5,15) (4,10) (3,6)

What is

1. linear

2. nonlinear?

400

Do these coordinated pairs make a Function?

(-2,15) (0,20) (0,10) (2,5) (4,20)

What is no?

500

Daily Double

A store sells previously viewed movies. The table show the cost for buying movies 1,2,3 and 4.


movies     cost

1             $10

2             $18

3             $24

4             $28


1. This is a function

yes or no

2. Describe the pattern.

3. How does the cost per movie change as you buy movie as you buy more movies?

1. What is Yes?

2. What is each input increase of 1, the output increases by $2 than the previous increase?

3. What is for each additional movie you buy your cost per movie decreases by $1?

500

Daily Double

You want to take a 2 hour hour airboat tour. 

Gator tours $35 boarding fee plus $5 each 1/2 half. All rating per person.

Snake tours $25 per hour. All rates per person.

1. write a function that represents the cost G of a tour at Gator tours

2. Write a function that represents the cost of S a tour at Snake tours.

3. Which is the better deal?

What is

1. G=35+10h

2. S=25h

3. snake tours; For 2 hours, Gator tour cost $55 and Snake tours cost $50?


500

Daily Double 

The heat index is calculated by using the relative humidity and temperature. For every one 1 degree increase in the temperature from 94 degrees F to 98 degrees F at 75% relative humidity , the heat index rises 4 degrees F. 


1. Write a linear function that represents this situation.

2. Estimate the heat index if the temperature is 100 degrees F.

What is

1. H=4t-254

2. 146 degrees F

500
Tree A is 5 feet tall and grows at a rate of 1.5 feet per year. The table show the height h (in feet) of tree B after x amount of years


Years,x         Height,h

0                  5

1                  11

4                  17

9                  23

1. Is this a linear or nonlinear function

2. Which tree is taller in 10 years

What is 

1. nonlinear

2. Tree B?

500
Write an equation for this function


input x    output y

1               8

2               9

3              10  

4              11

What is y=x+7