B
College Algebra – Chapter 2 Exam
Name
Directions: A calculator MAY be used on this test. Show all work and reasoning to receive full credit.
For Questions 13 & 14, use the function 𝑓(𝑥) = 3𝑥 2 − 14𝑥 + 8 to algebraically determine the following.
12) If f (x) = 13, find the value(s) of x.
What are the point(s) on the graph?
13) Find all intercepts of the graph of f.
Write you answer as points.
14) For 𝑓(𝑥) = 4𝑥 2 − 2𝑥 + 6 and 𝑔(𝑥) = 2𝑥 2 − 3, determine the following (simplify fully).
a) f  g
b) f  g
c) f (3  x )
15) Determine and simplify the difference quotient,
f ( x  h)  f ( x)
, for the function𝑓(𝑥) = 3𝑥 2 − 7𝑥 + 5.
h
B
For Questions 14 & 15, use the function 𝑓(𝑥) = 2𝑥 3 + 4𝑥 2 − 5 to determine the following.
16) Average rate of change from -6 to 8.
(no decimal approximations)
17) Any local maxima and local minima.
18) Given the function f ( x )  3x 2  x find the equation of the secant line containing (−2, 𝑓(−2)) and
(3, 𝑓(3)).
19) Determine the equation of each graph.
a)
f ( x) 
b)
f ( x) 
B
20) Researchers have determined that the number of College Algebra students who suffer from "panic
headaches" while taking an in-class test depends on the number of word problems on the test. Last semester,
observations yielded the following data:
Number of word problems (W)
2
6
9
11
Number of headaches (h)
8
21 27 36
a) Determine the best-fit linear function for the data (round answers to the nearest thousandths).
b) Use the linear function to determine the number of word problems on an exam if 40 students had headaches.
(If you use your calculator and get an error, make the Xmax in your window larger)
21) A farmer has 500 yards of fencing to enclose a rectangular field. One side will be against a river, and will
therefore not need any fencing. The width of the field is represented by the side perpendicular to the river.
a) Draw a diagram and express the area A of the field as a function of the width w.
c) What width and length will maximize the area of the garden? What is the maximum area?
Bonus) A rectangle is inscribed in a semi-circle of radius 9. Express the total area of the rectangle as a function
of the x-coordinate of point P shown below. Determine the value of x that will maximize the area of the
rectangle.