NAME:
PERIOD:
NOTE: There are intentionally no room below to work the problems. Attach all sheets of paper use to
solve the following problems.
Problem 1:
f is a linear function. Values of x and f(x) are given in the table below; complete the table.
x
f(x)
-3
17
0
--
--
1
4
-18
7
--
--
-30
Problem 2:
A family of linear functions is given by
f(x) = mx + (3 - 2 m)
where x is the independent variable and m is a constant.
a) Graph f for m = 0, 1, 2, -3 and -5
b) What do all the graphs in part a) have in common?
c) Justify your answer to part b) analytically.
d) Write the equation of the family of functions whose graphs pass by the same point
(- 2 , - 4). Hint: Utilize Point Slope Form
Problem 3:
A high school had 1200 students enrolled in 2013 and 1500 students in 2016. If the student population P
grows as a linear function of time t, where t is the number of years after 2013.
a) How many students will be enrolled in the school in 2020?
b) Find a linear function that relates the student population to the time t.
Problem 4:
The graph shown below is that of the linear function that relates the value V (in $) of a car to its age t,
where t is the number of years after 2000.
.
a) Find the slope and interpret it.
b) What will be the value of the car in the year 2010?
Problem 5:
A 500-liter tank full of oil is being drained at the constant rate of 20 liters par minute.
a) Write a linear function V for the number of liters in the tank after t minutes (assuming that the
drainage started at t = 0).
b) Find the V and the t intercepts and interpret them.
e) How many liters are in the tank after 11 minutes and 45 seconds?
Problem 6:
The cost of producing x tools by a company is given by
C(x) = 1200 x + 5500 (in $)
a) What is the cost of 100 tools?
b) What is the cost of 101 tools?
c) Find the difference between the cost of 101 and 100 tools.
d) Find the slope of the graph of C?
e) Interpret the slope.
Problem 7:
A 50-meter by 70-meter rectangular garden is surrounded by a walkway of constant width x meters.
a) Write the outside perimeter P in terms of x.
b) Find the slope of the graph of P.
c) What is the meaning of the slope found in b)?
Problem 8:
A driver starts a journey with 25 gallons in the tank of his car. The car burns 5 gallons for every 100
miles. Assuming that the amount of gasoline in the tank decreases linearly,
a) write a linear function that relates the number of gallons G left in the tank after a journey of x miles.
b) What is the value and meaning of the slope of the graph of G?
c) What is the value and meaning of the x intercept?
Problem 9:
A rectangular wire frame has one of its dimensions moving at the rate of 0.5 cm / second. Its width is
constant and equal to 4 cm. If at t = 0 the length of the rectangle is 10 cm,
a) what is the length at time t.
b) Write a formula for the area A of the rectangle in terms of t.
c) Write a formula for the perimeter P of the rectangle in terms of t.
c) As x increases, which one, the perimeter or the area, increases faster?
NOTE: The grade on this assignment is a Daily Grade. Additionally, this grade can be used to replace
your lowest Quiz grade should this grade be higher than your lowest quiz grade.
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