a. Complete the table below. In the third column, show your work as - - PowerPoint PPT Presentation

DAY 111 - PROVE THAT LINEAR

FUNCTIONS GROW BY EQUAL DIFFERENCES AND THAT EXPONENTIAL FUNCTIONS GROW BY EQUAL FACTORS

• a. Complete the table below. In the third column, show

your work as demonstrated. What do you notice about the 3rd column of the table?

x y = 3x + 2 𝚬y

1 5 … 2 8 8 – 5 = 3 3 4 5

• b. Complete the table below, showing your work as above.

What do you notice about the 3rd column of the table? What is the graphical interpretation of this?

x y = ax + b 𝚬y

1 a  1 + b … 2 a  2 + b a  2 + b – (a  1 + b) = a 3 4 5

• c. Let

. Let x be any particular x-

• value. Show that of x is increased by 1, the

corresponding 𝚬y is constant; What is this constant?

• d. Does a) server as an example of the result in c)?

Explain.

b ax y  

For each representation of a function, decide if the function is linear, exponential, or neither. Give at least 2 reasons for your answer. 1.

Reasons may vary

• 2. Tennis tournament

There are 4 players remaining after 5 rounds.

Exponential

Round Numbers

• f

Players left 1 2 3 4 5

64 32 16 8 4

3. Linear

• 4. This function is decreasing at a constant rate.

Linear Exponential 5.

x y 4 

• 6. A person’s height as a function of a person’s age (from

age 0 to 100) Exponential 7. Linear 8. Linear

7 4 3    y x

x y

• 2

23 5 2

• 13

4

• 31

6

• 49

9. Neither

• 10. The number of cell phone users in Centerville as a

function of years, if the number of users is increasing by 75% each year. Exponential

Height in inches Shoe Size 62 6 74 13 70 9 67 11 53 4 58 7

11. Exponential

• 12. The time it takes you to get to work as a function the

speed at which you drive. Linear

13. Exponential

• 14. Each point on the graphs Is exactly 1/3
• n the previous point.

Exponential

2

7x y 

15. Neither 16. Exponential

2)

• (n

1)

• (n

(n) 7 (2) 7 (1) + f = f ,f = ,f = f

(n) 3 2 1) + (n 1 (o) f = f , = f