4-5 Writing a function
rule
MATH 8 PLUS
MR. DIXON
Example #1; Writing a Function Rule
A landfill has 50,000 tons of waste in it. Each month it accumulates an average
of 420 more tons of waste. What is the function rule that represents the total
amount of waste after m months?
Model: Total Waste
is 50,000 tons plus
of waste
420 tons of waste
each month
times
Define: Let T = the total waste, and let m = the number of months.
Equation:
T = 50,000 + 420m
number of
months
Example #1; Writing a Function Rule
You can estimate the temperature by counting the number of chirps of the snowy tree cricket.
The outdoor temperature is about 400F more than one fourth the number of chirps the
cricket makes in one minute. What is the function rule that represents this situation?
Model:
temperature
is 400F more than
1
4
of
the number of chirps
in 1 minute
Define: Let T = temperature. Let n = the number of chirps in 1 min.
Equation:
T = 40 + 1n
4
Example #2; Writing and Evaluating a
Function Rule
A kennel charges $15 per day to board dogs. Upon arrival, each dog must have a flea
bath that costs $12. Write a function rule for the total cost for n days of boarding
plus a bath. How much does a 10-day stay cost?
Define:
Let T = total cost. Let n = the number of days.
Equation:
T = 15(n) + 12
Evaluate T for n = 10:
T = 15(10) + 12
T = 150 + 12
Answer: The cost for
T = 162
a 10-day stay is $162.
Example #3; Writing a Nonlinear
Function Rule
Write a function rule for the area of a triangle whose height is 4 in. more than twice
the length of its base. What is the area of the triangle when the length of its base
is 16 in.?
Define:
Let h = height of the triangle. Let b = the base of the triangle.
Write:
h = 2b + 4
Equation:
A = 1(b)(h)
2
Example #3; continued
Write a function rule for the area of a triangle whose height is 4 in. more than twice
the length of its base. What is the area of the triangle when the length of its base
is 16 in.?
Find the area with a base of 16 in.
A = 1 (b)(2b + 4) (2) A = 1 (2b2 + 4b) (2)
2
A = b2 + 2b
2
2A = 2b2 + 4b
A = 1 (2b2 + 4b)
A = 162 + 2(16)
2
2
2
2
A = 256 + 32
A = b2 + 2b
Function Rule:
A = 288 in2
Assignment
Pgs. 265 – 265 (1 – 11) All; (12, 14, 16, & 18)
Show all work to receive full credit.
Make sure your function rule relates to the problem.
Calculators may be used.