D AY 111 - P ROVE 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 3 rd column of the table? x y = 3x + 2 𝚬 y 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 3 rd column of the table? What is the graphical interpretation of this? x y = ax + b 𝚬 y a 1 + b 1 … a 2 + b a 2 + b – (a 1 + b) = a 2 3 4 5
c. Let . Let x be any particular x- y ax b value. Show that of x is increased by 1, the corresponding 𝚬 y is constant; What is this constant? d. Does a) server as an example of the result in c)? Explain.
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 Round 1 2 3 4 5 Numbers of Players left 64 32 16 8 4 There are 4 players remaining after 5 rounds. Exponential
y x 4 3. Linear 4. This function is decreasing at a constant rate. Linear Exponential 5.
6. A person’s height as a function of a person’s age (from age 0 to 100) Exponential 3 x 4 y 7 7. Linear 8. x y Linear -2 23 0 5 2 -13 4 -31 6 -49
Height in 9. Shoe Size inches Neither 62 6 74 13 70 9 67 11 53 4 58 7 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
11. Exponential 12. The time it takes you to get to work as a function the speed at which you drive. Linear
y 2 7 x 13. Exponential 14. Each point on the graphs Is exactly 1/3 on the previous point. Exponential
f (1) = 7 ,f (2) = 7 ,f (n) = f (n - 1) + f (n - 2) 15. Neither 2 f (o) = 1 , f (n + 1) = f (n) 16. 3 Exponential
Recommend
More recommend
