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Unit 3 – Modeling with Linear Functions – Quiz
1. Which scenario could be modeled by a linear function?
a. the population of a city that is growing by 3% each year
b. the amount of carbon in a sample that is decaying by half every 6 hours
c. the number of calories burned when running at a constant speed
d. the height of a rocket 6 hours after takeoff
2. Given the data set below, would a linear function be appropriate to model the relationship
between x and g(x)? Explain why or why not.
x g(x)
0 0.27
2 0.55
7 0.83
10 1.11
3. Given the data set below, would a linear function be appropriate to model the relationship
between x and h(x)? Explain why or why not.
x H(x)
0 1.44
2 3.34
7 8.09
10 10.94
4. Consider this function in recursive form.
f(1) = -3
f(n) = f(n – 1) + 3; n ≥ 2
Select the equivalent explicit function for n ≥ 1.
a.
b.
c.
d.
f(n) = 3(n – 1)
f(n) = -3(n – 1)
f(n) = n + 3
f(n) = 3n – 6
5. A theater needs to place seats in rows. The function, f(r), as shown below, can be used to
determine the number of seats in each row, where r is the row number.
f(1) = 8
f(r) = f(r – 1) + 3
Use the function to complete the table indicating the number of seats in each row for the first four
rows of the theater.
Row Number Number of Seats
1
2
3
4
6. Consider this function in explicit form.
f(n) = 3n – 4; n ≥ 1
Select the equivalent recursive function.
a. f(1) = -1
f(n) = f(n – 1) + 3; n ≥ 2
b. f(1) = -1
f(n) = 3f(n – 1); n ≥ 2
c. f(0) = -4
f(n) = 3f(n – 1); n ≥ 2
d. f(0) = -4
f(n) = f(n – 1) + 3; n ≥ 2
7. For the function g(x) = x2, find the average rate of change from x = 2 to x = 5.
Solutions:
1. C
2. Yes, it is linear because it has a constant slope of 0.28.
3. Slope is constant at 0.95, so it is linear.
4. D
Row Number Number of Seats
1
8
2
11
3
14
4
17
5.
6. A
7. (g(5) – g(2))/(5 – 2) = 7